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第1行： − 此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。+ − 此词条由Miyasaki初步审校完成。+ − + − {{Redirect|Subordinate|other uses|Subordination (disambiguation){{!}}Subordination}}+ − − {{short description|System of elements that are subordinated to each other}} − − A '''hierarchy''' (from the [[Ancient Greek|Greek]] ἱεραρχία ''hierarkhia'', "rule of a high priest", from ''[[ordinary (officer)|hierarkhes]]'', "president of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as [[philosophy]], [[mathematics]], [[computer science]], [[organizational theory]], [[systems theory]], and the [[social sciences]] (especially [[political philosophy]]). − − A hierarchy (from the Greek ἱεραρχία hierarkhia, "rule of a high priest", from hierarkhes, "president of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as philosophy, mathematics, computer science, organizational theory, systems theory, and the social sciences (especially political philosophy). − − − A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a [[path (graph theory)|path]]. All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two [[co-worker]]s or [[Comrade|colleague]]s; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. [[Heterarchy]] is one such form. − − A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path. All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers or colleagues; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form. 第23行：
第12行： − − {{see also| Glossary of graph theory| Taxonomy (general)| Structure}} − − Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see [[#Visualization|below]]). − − Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below). − − − − In an organizational context, the following terms are often used related to hierarchies:<ref name="Dawkins"/><ref name="Architecture"/> − − In an organizational context, the following terms are often used related to hierarchies: − − * '''[[Non-physical entity|Object]]''': one entity (e.g., a person, department or [[concept]] or element of arrangement or member of a set) − * '''[[System]]''': the entire set of objects that are being arranged hierarchically (e.g., an administration) − * '''[[Dimension]]''': another word for "system" from on-line analytical processing (e.g. cubes) − * '''[[Element (mathematics)|Member]]''': an (element or object) at any (level or rank) in a (class-system, taxonomy or dimension) − **'''[[Ranking|Rank]]''': the relative [[value (ethics)|value]], worth, [[complexity]], [[Power (philosophy)|power]], importance, [[authority]], level etc. of an object − **'''[[wikt:level#Noun|Level]] or Tier''': a set of objects with the same rank OR importance − **'''[[Order of precedence|Ordering]]''': the arrangement of the (ranks or levels) − **'''Hierarchy''': the arrangement of a particular set of members into (ranks or levels). Multiple hierarchies are possible per (dimension taxonomy or Classification-system), in which selected levels of the dimension are omitted to flatten the structure − **'''[[wikt:hierarch|Hierarch]]''', the apex of the hierarchy, consisting of one single orphan (object or member) in the top level of a dimension. The root of an inverted-tree structure − **'''[[wikt:member|Member]]''', a (member or node) in any level of a hierarchy in a dimension to which (superior and subordinate) members are attached − **'''[[wikt:orphan|Orphan]]''', a member in any level of a dimension without a parent member. Often the apex of a disconnected branch. Orphans can be grafted back into the hierarchy by creating a relationship (interaction) with a parent in the immediately superior level − **'''[[wikt:leaf|Leaf]]''', a member in any level of a dimension without subordinates in the hierarchy − **'''[[wikt:neighbour|Neighbour]]''': a member adjacent to another member in the same (level or rank). Always a peer. − **'''[[Superior (hierarchy)|Superior]]''': a higher level or an object ranked at a higher level (A parent or an ancestor) − **'''[[wikt:subordinate|Subordinate]]''': a lower level or an object ranked at a lower level (A child or a descendant) − ** '''[[Family of sets|Collection]]''': all of the objects at one level (i.e. Peers) − ** '''[[wikt:peer|Peer]]''': an object with the same rank (and therefore at the same level) − ** '''[[Interpersonal relationship|Interaction]]''': the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair) − *** a '''direct''' interaction occurs when one object is on a level exactly one higher or one lower than the other (i.e., on a [[tree (graph theory)|tree]], the two objects have a line between them) − ** '''[[Distance (graph theory)|Distance]]''': the minimum number of connections between two objects, i.e., one less than the number of objects that need to be "crossed" to trace a [[path (graph theory)|path]] from one object to another − − ** '''[[wikt:Span|Span]]''': a [[qualitative data|qualitative]] description of the width of a level when diagrammed, i.e., the number of subordinates an object has − ** '''[[wikt:attribute|Attribute]]''': a heritable characteristic of (members and their subordinates) in a level (e.g. ''hair-colour'') − ** '''[[wikt:attribute-value|Attribute-value]]''': the specific value of a heritable characteristic (e.g. ''Auburn'') − − In a mathematical context (in [[graph theory]]), the [[Glossary of graph theory|general terminology]] used is different. − − In a mathematical context (in graph theory), the general terminology used is different. − − − Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with [[data structure]]s, objects are known as [[node (computer science)|nodes]], superiors are called [[parent node|parents]] and subordinates are called [[child node|children]]. In a business setting, a superior is a [[supervisor|supervisor/boss]] and a peer is a [[Comrade|colleague]]. − − Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with data structures, objects are known as nodes, superiors are called parents and subordinates are called children. In a business setting, a superior is a supervisor/boss and a peer is a colleague. 第136行：
第79行： − + − − [[Degree (graph theory)|Degree]] of [[Bifurcation theory|branching]] refers to the number of direct [[#Terminology|subordinates]] or children an object has (in graph theory, equivalent to the number of other [[vertex (graph theory)|vertices]] connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: ''linear'' and ''branching''. − Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: linear and branching. − + − In a '''linear hierarchy'''<!--per WP:R#PLA, this SHOULD be bold-->, the maximum degree is 1.<ref name="Dawkins"/> In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. Note that this is referring to the ''objects'' and not the ''levels''; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. An example of a linear hierarchy is the [[hierarchy of life]]. − − In a linear hierarchy, the maximum degree is 1. In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. Note that this is referring to the objects and not the levels; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. An example of a linear hierarchy is the hierarchy of life. − − − − − − In a '''branching hierarchy'''<!--per WP:R#PLA, this SHOULD be bold-->, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher).<ref name="Dawkins"/> For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy.<ref name="Dawkins"/> Branching hierarchies are present within numerous systems, including [[organization]]s and [[classification scheme]]s. The broad category of branching hierarchies can be further subdivided based on the degree. − − In a branching hierarchy<!--per WP:R#PLA, this SHOULD be bold-->, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy. Branching hierarchies are present within numerous systems, including organizations and classification schemes. The broad category of branching hierarchies can be further subdivided based on the degree. − − A '''flat hierarchy'''<!--per WP:R#PLA, this SHOULD be bold--> is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span.<ref name="Architecture">{{cite journal|last=Simon|first=Herbert A.|title=The Architecture of Complexity|journal=[[Proc. Am. Philos. Soc.]]|volume=106|issue=6|date=12 December 1962|pages=467–482|publisher=[[American Philosophical Society]]|issn=0003-049X|location=Philadelphia, Pennsylvania |jstor=985254 |citeseerx=10.1.1.110.961}}{{registration required}}</ref> Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, [[diamond]]s and [[graphite]] are flat hierarchies of numerous [[carbon]] atoms that can be further decomposed into subatomic particles. − − A flat hierarchy<!--per WP:R#PLA, this SHOULD be bold--> is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span. Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles. − − − An '''overlapping hierarchy'''<!--per WP:R#PLA, this SHOULD be bold--> is a branching hierarchy in which at least one object has two parent objects.<ref name="Dawkins"/> For example, a [[graduate student]] can have two [[research supervisor|co-supervisors]] to whom the student reports directly and equally, and who have the same level of authority within the [[university]] hierarchy (i.e., they have the same [[list of academic ranks|position]] or [[tenure]] status). − − An overlapping hierarchy<!--per WP:R#PLA, this SHOULD be bold--> is a branching hierarchy in which at least one object has two parent objects. For example, a graduate student can have two co-supervisors to whom the student reports directly and equally, and who have the same level of authority within the university hierarchy (i.e., they have the same position or tenure status). − − Possibly the first use of the English word "hierarchy" cited by the ''[[Oxford English Dictionary]]'' was in 1881, when it was used in reference to the three orders of three angels as depicted by [[Pseudo-Dionysius the Areopagite]] (5th–6th centuries). Pseudo-Dionysius used the related [[Ancient Greek|Greek]] word (ἱεραρχία ''hierarchia'') both in reference to the [[De Coelesti Hierarchia|celestial hierarchy]] and the [[ecclesiastical hierarchy]].<ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy<!-- Bot generated title -->]</ref> The Greek term ἱεραρχία means "rule of a high priest"<ref>[https://www.etymonline.com/word/hierarchy "hierarchy"]. [[Online Etymology Dictionary]].</ref> (from ἱεράρχης ''hierarches'', meaning "president of sacred rites, high-priest"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28era%2Frxhs ἱεράρχης], − Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>and that from ἱερεύς ''hiereus'', "priest"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28ereu%2Fs ἱερεύς], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref> and ἀρχή ''arche'', amongst others "first place or power, rule"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Da%29rxh%2F ἀρχή], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>),and Dionysius is credited with first use of it as an abstract noun. Since hierarchical churches, such as the [[Roman Catholicism|Roman Catholic]] (see [[Catholic Church hierarchy]]) and [[Eastern Orthodoxy|Eastern Orthodox]] churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with [[God in Christianity|God]] as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in [[secular]] settings. − − − Possibly the first use of the English word "hierarchy" cited by the Oxford English Dictionary was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία hierarchia) both in reference to the celestial hierarchy and the ecclesiastical hierarchy. The Greek term ἱεραρχία means "rule of a high priest" (from ἱεράρχης hierarches, meaning "president of sacred rites, high-priest" and that from ἱερεύς ''hiereus'', "priest"and ἀρχή ''arche'', amongst others "first place or power, rule"), and Dionysius is credited with first use of it as an abstract noun. Since hierarchical churches, such as the Roman Catholic (see Catholic Church hierarchy) and Eastern Orthodox churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with God as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in secular settings. − + − − = = = 视觉表现层次结构 = = = < ! -- 如果你更改这个部分的标题，请也更改文章中链接到它的 wikileink！--> 第197行：
第109行： − A hierarchy is typically depicted as a [[pyramid (geometry)|pyramid]], where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole.<ref>{{cite book | title=Regions of War and Peace | publisher=University of Cambridge | author=Douglas Lemke | year=2002 | location=Cambridge | pages=49}}</ref> For example, the few [[Board of Directors|Directors]] of a company could be at the [[apex (geometry)|apex]], and the [[Base (geometry)|base]] could be thousands of people who have no subordinates.+ − − A hierarchy is typically depicted as a pyramid, where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole. For example, the few Directors of a company could be at the apex, and the base could be thousands of people who have no subordinates. − − 层次结构通常被描述为金字塔形，其中高度代表层次状态而宽度代表该层的元素多寡。例如，一个公司的几个董事处于顶峰，而基层可能是成千上万没有下级的人。 − − − These pyramids are typically diagrammed with a [[tree structure|tree]] or [[triangle]] [[diagram]] (but note that not all triangle/pyramid diagrams are hierarchical; for example, the 1992 [[History of USDA nutrition guides#Food Guide Pyramid|USDA food guide pyramid]]), both of which serve to emphasize the size differences between the levels. An example of a triangle diagram appears to the right. An [[organizational chart]] is the diagram of a hierarchy within an [[organization]], and is depicted in tree form in {{section link|#Organizations}}, below. − These pyramids are typically diagrammed with a tree or triangle diagram (but note that not all triangle/pyramid diagrams are hierarchical; for example, the 1992 USDA food guide pyramid), both of which serve to emphasize the size differences between the levels. An example of a triangle diagram appears to the right. An organizational chart is the diagram of a hierarchy within an organization, and is depicted in tree form in , below. − − − More recently, as computers have allowed the storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include [[fractal]] maps, [[treemapping|TreeMaps]] and [[Radial tree|Radial Trees]]. − − More recently, as computers have allowed the storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include fractal maps, TreeMaps and Radial Trees. − − In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of [[visual hierarchy]]. Visual hierarchy is also important for proper organization of files on computers. − − In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of visual hierarchy. Visual hierarchy is also important for proper organization of files on computers. − − − An example of visually representing hierarchy is through the Nested clusters. The Nested clusters represents hierarchical relationships by using layers of information. The child element is within the parent element, such as in a [[Venn diagram]]. This structure of representing hierarchy is most effective in representing simple relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located. − − An example of visually representing hierarchy is through the Nested clusters. The Nested clusters represents hierarchical relationships by using layers of information. The child element is within the parent element, such as in a Venn diagram. This structure of representing hierarchy is most effective in representing simple relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located. − − For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at the left and descending on the right. The child elements are towards the bottom of the stairs and the parent elements are at the top. This structure is effective when representing more complicated hierarchies where steps are not placed in obvious sequences. Further steps are concealed unless all of the steps are revealed in sequence. In the computer desktop example, a file that is being sought after can only be found once another file is opened. The link for the desired file is within another document. All the steps must be completed until the final destination is reached. − − For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at the left and descending on the right. The child elements are towards the bottom of the stairs and the parent elements are at the top. This structure is effective when representing more complicated hierarchies where steps are not placed in obvious sequences. Further steps are concealed unless all of the steps are revealed in sequence. In the computer desktop example, a file that is being sought after can only be found once another file is opened. The link for the desired file is within another document. All the steps must be completed until the final destination is reached. 第242行：
第128行： − In plain English, a hierarchy can be thought of as a [[Set (mathematics)|set]] in which:<ref name="Dawkins">{{cite conference|last=Dawkins|first=Richard|authorlink=Richard Dawkins|title=Hierarchical organization: a candidate principle for ethology|conference=Growing points in ethology: based on a conference sponsored by St. John's College and King's College, Cambridge|editor1=Bateson, Paul Patrick Gordon |editor2=Hinde, Robert A.|year=1976|publisher=Cambridge University Press|location=Cambridge, England|isbn=0-521-29086-4|pages=7–54}}</ref>+ − − In plain English, a hierarchy can be thought of as a set in which: − − 在日常英语中，层次可以被看作是一个集合，其中: − − # No element is superior to itself, and − # One element, the ''hierarch'', is superior to all of the other elements in the set. − − The first requirement is also interpreted to mean that a hierarchy can have no [[Cycle (graph theory)|circular relationships]]; the association between two objects is always [[Transitive relation|transitive]]. − − The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive. − The second requirement asserts that a hierarchy must have a leader or [[root node|root]] that is common to all of the objects. − − The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects. − − {{Main|层次（数学） Hierarchy (mathematics)}} − − Mathematically, in its most general form, a hierarchy is a [[partially ordered set]] or ''poset''.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The [[#Terminology|system]] in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting [[#Terminology|levels]] is referred to as a [[class (set theory)|class]]. − − |isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class. − − "Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a [[combinatorial]] [[object]].--> − − "Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. <!--Mathematically, a hierarchy can be depicted as a combinatorial object.--> − − Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: − − Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example: − − − (2 + 5) × (7 - 4). − − (2 + 5) × (7 - 4). − − (2 + 5) × (7 - 4). − − In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations. − − In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations. 第302行：
第149行： − + − − = = = 嵌套层次结构 = = = = < ! -- 如果您更改此标题，请更改链接到该标题的文章中的 wiki 链接! -- > − − [[File:Russian-Matroshka no bg.jpg|200px|right|thumb|[[Matryoshka doll]]s, also known as ''nesting dolls'' or ''Russian dolls''. Each doll is encompassed inside another until the smallest one is reached. This is the concept of ''nesting''. When the concept is applied to [[set (mathematics)|sets]], the resulting ordering is a ''nested hierarchy''.]] − − [[Matryoshka dolls, also known as nesting dolls or Russian dolls. Each doll is encompassed inside another until the smallest one is reached. This is the concept of nesting. When the concept is applied to sets, the resulting ordering is a nested hierarchy.]] − − '''<font color="#ff8000">玛特罗什卡套娃 Matryoshka Doll</font>'''，又称嵌套娃娃或俄罗斯套娃。每个洋娃娃都被包裹在另一个洋娃娃里面，直到最小的洋娃娃。这就是嵌套的概念。当这个概念应用于集合时，其结果排序是一个嵌套的层次结构。 − − A nested hierarchy or ''inclusion hierarchy'' is a hierarchical ordering of [[nested set]]s.<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref> The concept of nesting is exemplified in Russian [[matryoshka doll]]s. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:+ − + − A nested hierarchy or inclusion hierarchy is a hierarchical ordering of nested sets.<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref> The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example: − − 嵌套层次结构或包含层次结构，是指嵌套集的层次结构排序。嵌套的概念在俄罗斯套娃中得到体现。每个玩偶都被另一个玩偶包裹着，一直到最外层的。外部的套娃包含所有其内部的玩偶，往外一层的玩偶也包含所有其内部剩余的玩偶，如此反复。套娃结构是一个每层都只有一个对象的嵌套层次结构，例如在套娃中同样大小的玩偶只有一个；广义的嵌套层次可以每层都有多个对象，但每层里的对象都只有一个父级对象。嵌套层次一般概念的论证及数学表达如下： + − − <math> \text{square} \subset \text{quadrilateral} \subset \text{polygon} \subset \text{shape} \, </math> − − − A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can ''only'' be a quadrilateral; it can never be a [[triangle]], [[hexagon]], etc. − − A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be a quadrilateral; it can never be a triangle, hexagon, etc. − − − Nested hierarchies are the organizational schemes behind [[Taxonomy (general)|taxonomies]] and systematic classifications. For example, using the original [[Linnaean taxonomy]] (the version he laid out in the 10th edition of ''[[Systema Naturae]]''), a human can be formulated as:<ref>{{cite book|title=Systema naturae per regna tria naturae :secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis|last=Linnaei|first=Carl von|authorlink=Carl Linnaeus|year=1959|edition=10th|language=Latin|url=https://www.biodiversitylibrary.org/bibliography/542#|location=[[Stockholm]]|publisher=Impensis Direct|isbn=0-665-53008-0|accessdate=2011-09-24}}</ref> − − Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of Systema Naturae), a human can be formulated as: − − − − − − Taxonomies may change frequently (as seen in [[biological classification|biological taxonomy]]), but the underlying concept of nested hierarchies is always the same. − − Taxonomies may change frequently (as seen in biological taxonomy), but the underlying concept of nested hierarchies is always the same. − − − In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of [[self-similarity]] and [[recursion]]. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.<ref name=Corballis>{{cite book |first=Michael |last=Corballis |title=The Recursive Mind |publisher=Princeton University Press |year=2011 |isbn=978-0691145471}}</ref> − − In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic. − − A containment hierarchy is a direct extrapolation of the [[#Nested hierarchy|nested hierarchy]] concept. All of the ordered sets are still nested, but every set must be "[[strict subset|strict]]"—no two sets can be identical. The shapes example above can be modified to demonstrate this: − − A containment hierarchy is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be "strict"—no two sets can be identical. The shapes example above can be modified to demonstrate this: 第374行：
第181行： − − − The notation <math> x \subsetneq y \, </math> means ''x'' is a subset of ''y'' but is not equal to ''y''. − − The notation <math> x \subsetneq y \, </math> means x is a subset of y but is not equal to y. − − − − A general example of a containment hierarchy is demonstrated in [[inheritance (computer science)|class inheritance]] in [[object-oriented programming]]. − − A general example of a containment hierarchy is demonstrated in class inheritance in object-oriented programming. 第392行：
第188行： − − Two types of containment hierarchies are the ''subsumptive'' containment hierarchy and the ''compositional'' containment hierarchy. A subsumptive hierarchy "[[wikt:subsume|subsumes]]" its children, and a compositional hierarchy is "[[wikt:composed|composed]]" of its children. A hierarchy can also be both subsumptive ''and'' compositional{{example needed|date=August 2018}}.<ref name="AI industrial">{{cite encyclopedia|title=Industrial and Engineering Applications of Artificial Intelligence and Expert Systems|last=Kopisch|first=Manfred|last2=Günther|first2=Andreas|doi=10.1007/BFb0024994|editor-last=Belli|editor-first=Fevzi|encyclopedia=Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings|year=1992|publisher=[[Springer Science+Business Media|Springer]]|pages=424–427|isbn=3-540-55601-X|series=Lecture Notes in Computer Science Series|volume=602|issn=0302-9743|editor6-last=Radermacher|editor8-first=Franz-Josef|chapter=Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control}}</ref> − − Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy "subsumes" its children, and a compositional hierarchy is "composed" of its children. A hierarchy can also be both subsumptive and compositional. − − A ''[[Category theory|subsumptive]]'' containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "[[is-a|IS-A]] hierarchy".<ref name="Lehmann"/><ref name="ibm">{{cite web|url=http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|archive-url=https://archive.today/20130103052727/http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|url-status=dead|archive-date=3 January 2013|title=Compositional hierarchy|work=WebSphere Transformation Extender Design Studio|accessdate=9 October 2009}}</ref><ref name="sys model">{{cite book|chapter=An advanced modeling environment based on a hybrid AI-OR approach|chapterurl=https://books.google.com/books?id=ds2eIQ6XZy0C&pg=PA366|pages=366–75|last=Funke|first=Birger|last2=Sebastian|first2=Hans-Jürgen|title=Systems modelling and optimization: proceedings of the 18th IFIP TC7 conference|volume=396|series=Research notes in mathematics series|editor1-last=Polis|editor1-first=Michael P.|editor2-last=Dontchev|editor2-first=Asen L.|editor3-last=Kall|editor3-first=Peter|editor4-last=Lascieka|editor4-first=Irena|editor5-last=Olbrot|editor5-first=Andrzej W.|publisher=[[CRC Press]]|year=1999|isbn=978-0-8493-0607-5}}</ref> The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is part of the level ''Mammalia'' "is a" member of the level ''Animalia''; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "[[concept]]s".<ref name="sys model"/> For example, with the Linnaean hierarchy outlined above, an entity name like ''Animalia'' is a way to group all the species that fit the [[wikt:conceptualization|conceptualization]] of an animal. − − A subsumptive containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "IS-A hierarchy". The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is part of the level Mammalia "is a" member of the level Animalia; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "concepts". For example, with the Linnaean hierarchy outlined above, an entity name like Animalia is a way to group all the species that fit the conceptualization of an animal. − + − A ''compositional'' containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts.<ref name="Parsons">{{cite book|last=Parsons|first=David|title=Object Oriented Programming in C++|publisher=Cengage Learning|year=2002|pages=110–185|isbn=0-8264-5428-3}}</ref> Most engineered structures, whether natural or artificial, can be broken down in this manner. − A compositional containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts. Most engineered structures, whether natural or artificial, can be broken down in this manner.+ − <font color="#32CD32">构成性包容层次结构 Compositional containment hierarchy</font>是构成系统的各个部分的顺序——系统是由这些部分“构成”的。大多数工程结构，无论是自然的还是人工的，都可以用这种方式分解。 − − − − The compositional hierarchy that every person encounters at every moment is the [[hierarchy of life]]. Every person can be reduced to [[organ system]]s, which are composed of [[organ (anatomy)|organs]], which are composed of [[tissue (biology)|tissues]], which are composed of [[cells (biology)|cells]], which are composed of [[molecule]]s, which are composed of [[atom]]s. In fact, the last two levels apply to all [[matter]], at least at the [[macroscopic scale]]. Moreover, each of these levels inherit all the properties of their [[#Terminology|children]]. − − The compositional hierarchy that every person encounters at every moment is the hierarchy of life. Every person can be reduced to organ systems, which are composed of organs, which are composed of tissues, which are composed of cells, which are composed of molecules, which are composed of atoms. In fact, the last two levels apply to all matter, at least at the macroscopic scale. Moreover, each of these levels inherit all the properties of their children. − − − In this particular example, there are also ''[[emergent properties]]''—functions that are not seen at the lower level (e.g., [[cognition]] is not a property of [[neuron]]s but is of the [[Human brain|brain]])—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not a required general property. These ''level hierarchies'' are characterized by bi-directional [[Causality|causation]].<ref name="natsocsci-ch4"/> ''Upward causation'' involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. ''[[Downward causation]]'' refers to the effect that the incorporation of entity ''x'' into a higher-level entity can have on ''x'''s properties and interactions. Furthermore, the entities found at each level are ''[[autonomous]]''. − − In this particular example, there are also emergent properties—functions that are not seen at the lower level (e.g., cognition is not a property of neurons but is of the brain)—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not a required general property. These level hierarchies are characterized by bi-directional causation. Upward causation involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. Downward causation refers to the effect that the incorporation of entity x into a higher-level entity can have on xs properties and interactions. Furthermore, the entities found at each level are autonomous. − + − − = = 上下文和应用 = = < ! ——如果你更改了这个部分的标题，请也更改文章中链接到它的 wikileink！--> − According to Kulish, V. V. (2002), almost every system of organization applied to the world is arranged hierarchically.<ref name="electrodynamics">{{cite book|title=Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics|last=Kulish|first=V. V.|isbn=1-4020-0757-4|year=2002|volume=1|publisher=[[Springer Science+Business Media|Springer]]|pages=xvii–xx; 49–71}}</ref> By their common definitions, every [[nation]] has a government and every government is hierarchical.<ref>{{Cite book|contribution=government|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/government?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref><ref>{{Cite book|contribution=nation|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/nation?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref> Socioeconomic systems are stratified into a social hierarchy (the [[social stratification]] of societies), and all [[systematic name|systematic classification schemes]] ([[Taxonomy (general)|taxonomies]]) are hierarchical. Most [[organized religion]]s, regardless of their internal governance structures, operate as a hierarchy under [[God]]. Many [[Christian denomination]]s have an [[autocephalous]] [[ecclesiastical hierarchy]] of leadership. Families are viewed as a hierarchical structure in terms of [[cousinship]] (e.g., first cousin once removed, second cousin, etc.), [[ancestry]] (as depicted in a [[family tree]]) and [[inheritance]] ([[order of succession|succession]] and [[heir]]ship). All the requisites of a well-rounded life and [[lifestyle (sociology)|lifestyle]] can be organized using [[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]]. [[Learning]] must often follow a hierarchical scheme—to learn [[differential equation]]s one must first learn [[calculus]]; to learn calculus one must first learn [[elementary algebra]]; and so on. Even [[nature]] itself has its own hierarchies, as numerous schemes such as [[Linnaean taxonomy]], the [[biological organisation|organization of life]], and [[biomass pyramid]]s attempt to document. Hierarchies are so infused into daily life that they are viewed as trivial.<ref name="Dawkins"/><ref name="electrodynamics"/> − − According to Kulish, V. V. (2002), almost every system of organization applied to the world is arranged hierarchically. By their common definitions, every nation has a government and every government is hierarchical. Socioeconomic systems are stratified into a social hierarchy (the social stratification of societies), and all systematic classification schemes (taxonomies) are hierarchical. Most organized religions, regardless of their internal governance structures, operate as a hierarchy under God. Many Christian denominations have an autocephalous ecclesiastical hierarchy of leadership. Families are viewed as a hierarchical structure in terms of cousinship (e.g., first cousin once removed, second cousin, etc.), ancestry (as depicted in a family tree) and inheritance (succession and heirship). All the requisites of a well-rounded life and lifestyle can be organized using Maslow's hierarchy of human needs. Learning must often follow a hierarchical scheme—to learn differential equations one must first learn calculus; to learn calculus one must first learn elementary algebra; and so on. Even nature itself has its own hierarchies, as numerous schemes such as Linnaean taxonomy, the organization of life, and biomass pyramids attempt to document. Hierarchies are so infused into daily life that they are viewed as trivial. 第445行：
第215行： + − While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most [[postal code]] systems are hierarchical. Using the [[Postal codes in Canada|Canadian postal code system]] as an example, the top level's binding concept is the "[[forward sortation area|postal district]]", and consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an [[#Degree_of_branching|overlapping hierarchy]], because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format ''A0A 0A0'' (the second and third letter position allow 20 objects each). Most [[library classification]] systems are also hierarchical. The [[Dewey Decimal Classification|Dewey Decimal System]] is regarded as infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point.<ref name="Dewey">{{cite journal|title=Tracking Nuclear Sources|date=May–June 2009|last=Walker|first=Randy|publisher=wellservicingmagazine.com|pages=28–30|url=http://wellservicingmagazine.com/sites/default/files/pdfmag/WSM_MAYJUN09.PDF}}{{dead link|date=November 2017 |bot=InternetArchiveBot |fix-attempted=yes}} See also [[Dewey Decimal Classification|Wikipedia article]].</ref> − − While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most postal code systems are hierarchical. Using the Canadian postal code system as an example, the top level's binding concept is the "postal district", and consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an overlapping hierarchy, because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format A0A 0A0 (the second and third letter position allow 20 objects each). Most library classification systems are also hierarchical. The Dewey Decimal System is regarded as infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point. − − 虽然上面的例子通常以层次形式清楚地描述并且很经典，但是层次结构也存在于许多分支结构并不是很明显的系统中。例如，大多数<font color="#ff8000">邮政编码 postal code</font>系统是分层的。以加拿大邮政编码系统为例，顶层的概念是“<font color="#ff8000">邮区 postal district</font>”，由18个对象(字母)组成。下一层是“<font color="#ff8000">地区 zone</font>”，其中的对象是数字0-9。这是重叠层次结构的一个例子，因为这10个对象中的每一个都有18个父对象。层次继续向下生成，理论上存在720万个 A0A 0A0 (第二个和第三个字母的位置每个允许20个对象)格式的唯一代码。大多数图书分类法系统也是分层级的。<font color="#ff8000">杜威十进制图书分类法 Dewey Decimal System</font>被认为是无限层次的，因为在小数点之后可以使用的数字数量是没有限制的。 − − − − [[File:Organizational chart.svg|thumb|200px|A simple [[hierarchical organization|organizational hierarchy]] depicted in the form of a [[tree structure|tree]]. Diagrams like this are called [[organizational chart]]s.]] − − organizational hierarchy depicted in the form of a tree. Diagrams like this are called organizational charts.]] 第463行：
第223行： − − {{Main|Organizational structure|Hierarchical organization}} − − − − [[Organization]]s can be structured as a [[dominance hierarchy]]. In an organizational hierarchy, there is a single person or group with the most [[power (philosophy)|power]] and [[authority]], and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including [[Forms of government|governments]], [[Company|companies]], [[militia]] and [[organized religion]]s. The units or persons within an organization are depicted hierarchically in an [[organizational chart]]. − − Organizations can be structured as a dominance hierarchy. In an organizational hierarchy, there is a single person or group with the most power and authority, and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including governments, companies, militia and organized religions. The units or persons within an organization are depicted hierarchically in an organizational chart. − − − In a [[reverse hierarchy]], the conceptual [[pyramid (geometry)|pyramid]] of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings. − − In a reverse hierarchy, the conceptual pyramid of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings. − − {{Main|Biological organisation#Fundamentals}} − − − − Empirically, we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity. [[Systems theory|System]] hierarchies analysis performed in the 1950s,<ref>{{harvnb|Evans|1951}}</ref><ref>{{harvnb|Evans|1956}}</ref> laid the empirical foundations for a [[Branches of science|field]] that would be, from the 1980s, '''hierarchical ecology'''.<ref>{{harvnb|Margalef|1975}}</ref><ref>{{harvnb|O'Neill|1986}}</ref><ref>{{harvnb|Wicken|Ulanowicz|1988}}</ref><ref>{{harvnb|Pumain|2006}}</ref><ref>{{harvnb|Jordan|Jørgensen|2012}}</ref> − − Empirically, we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity. System hierarchies analysis performed in the 1950s, laid the empirical foundations for a field that would be, from the 1980s, hierarchical ecology. − − The theoretical foundations are summarized by Thermodynamics. When [[biological systems]] are modeled as [[physical system]]s, in its most general abstraction, they are [[Thermodynamic system#Open system|thermodynamic open systems]] that exhibit [[self-organisation|self-organised]] behavior, and the [[Set theory|set/subset]] relations between [[dissipative structures]] can be characterized in a hierarchy. − − The theoretical foundations are summarized by Thermodynamics. When biological systems are modeled as physical systems, in its most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and the set/subset relations between dissipative structures can be characterized in a hierarchy. 第503行：
第238行： − {{Main|3D modeling}} − − [[Computer-generated imagery|CGI]] and [[computer animation]] [[computer program|programs]] mostly use hierarchies for models. On a [[3D computer graphics|3D]] [[3d modeling|model]] of a [[human]] for example, the [[chest]] is a [[parent]] of the upper left arm, which is a parent of the lower left arm, which is a parent of the [[hand]]. This is used in [[3D modeling|modeling]] and [[animation]] for almost everything built as a 3D [[Digital data|digital]] model. − − CGI and computer animation programs mostly use hierarchies for models. On a 3D model of a human for example, the chest is a parent of the upper left arm, which is a parent of the lower left arm, which is a parent of the hand. This is used in modeling and animation for almost everything built as a 3D digital model. − + − − Many grammatical theories, such as [[phrase-structure grammar]], involve hierarchy. − − Many grammatical theories, such as phrase-structure grammar, involve hierarchy. − − − [[Direct–inverse language]]s such as [[Cree language|Cree]] and [[Mapudungun language|Mapudungun]] distinguish subject and object on [[verb]]s not by different subject and object markers, but via a hierarchy of persons. − − Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on verbs not by different subject and object markers, but via a hierarchy of persons. − − − − In this system, the three (or four with [[Algonquian languages]]) persons are placed in a hierarchy of [[salience (language)|salience]]. To distinguish which is subject and which object, ''inverse markers'' are used if the object outranks the subject. − − In this system, the three (or four with Algonquian languages) persons are placed in a hierarchy of salience. To distinguish which is subject and which object, inverse markers are used if the object outranks the subject. − − − On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun phrase to which it refers, commonly crosses grammatical boundaries in non-hierarchical ways. − − On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun phrase to which it refers, commonly crosses grammatical boundaries in non-hierarchical ways. − + − − The structure of a musical composition is often understood hierarchically (for example by [[Heinrich Schenker]] (1768–1835, see [[Schenkerian analysis]]), and in the (1985) [[Generative theory of tonal music|Generative Theory of Tonal Music]], by composer [[Fred Lerdahl]] and linguist Ray [[Jackendoff]]). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or [[Ursatz]], which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature. − − The structure of a musical composition is often understood hierarchically (for example by Heinrich Schenker (1768–1835, see Schenkerian analysis), and in the (1985) Generative Theory of Tonal Music, by composer Fred Lerdahl and linguist Ray Jackendoff). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or Ursatz, which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature. − − − The [[pitch (music)|pitches]] and [[Musical form|form]] of [[Tonality|tonal]] music are organized hierarchically, all pitches deriving their importance from their relationship to a [[Tonic (music)|tonic]] [[Key signature|key]], and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. [[Susan McClary]] connects this specifically in the [[sonata-allegro form]] to the feminist hierarchy of gender (see above) in her book ''Feminine Endings'', even pointing out that primary themes were often previously called "masculine" and secondary themes "feminine." − − The pitches and form of tonal music are organized hierarchically, all pitches deriving their importance from their relationship to a tonic key, and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. Susan McClary connects this specifically in the sonata-allegro form to the feminist hierarchy of gender (see above) in her book Feminine Endings, even pointing out that primary themes were often previously called "masculine" and secondary themes "feminine." − + − − In the work of diverse theorists such as [[William James]] (1842–1910), [[Michel Foucault]] (1926–1984) and [[Hayden White]], important critiques of hierarchical [[epistemology]] are advanced. James famously asserts in his work "Radical Empiricism" that clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and intractable ambiguities, then scientific questions are often considered unresolved. − − In the work of diverse theorists such as William James (1842–1910), Michel Foucault (1926–1984) and Hayden White, important critiques of hierarchical epistemology are advanced. James famously asserts in his work "Radical Empiricism" that clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and intractable ambiguities, then scientific questions are often considered unresolved. − − − − Hierarchy in ethics emerged in Western Europe, West Asia and North Africa around the 1600s. In this aspect, the term hierarchy refers to how distinguishable they are from real to unreal. [[Feminists]], [[Marxists]], [[anarchists]], [[communists]], [[critical theorists]] and others, all of whom have multiple interpretations, criticize the hierarchies commonly found within human society, especially in social relationships. Hierarchies are present in all parts of society: in businesses, schools, families, etc. These relationships are often viewed as necessary. Entities that stand in hierarchical arrangements are animals, humans, plants, etc. − − Hierarchy in ethics emerged in Western Europe, West Asia and North Africa around the 1600s. In this aspect, the term hierarchy refers to how distinguishable they are from real to unreal. Feminists, Marxists, anarchists, communists, critical theorists and others, all of whom have multiple interpretations, criticize the hierarchies commonly found within human society, especially in social relationships. Hierarchies are present in all parts of society: in businesses, schools, families, etc. These relationships are often viewed as necessary. Entities that stand in hierarchical arrangements are animals, humans, plants, etc. 第577行：
第268行： − + − − [[File:Hierarchy Of Purposes.jpg|thumb|right|alt=|Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal.]] − − Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal. + − + − In [[ethics]], various [[virtues]] are enumerated and sometimes organized hierarchically according to certain brands of [[virtue theory]]. − − In ethics, various virtues are enumerated and sometimes organized hierarchically according to certain brands of virtue theory. − − − In some of these random examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts. There is a hierarchy of activities in human life: productive activity serves or is guided by the moral life; the moral life is guided by practical reason; practical reason (used in moral and political life) serves contemplative reason (whereby we contemplate God). Practical reason sets aside time and resources for contemplative reason. − − In some of these random examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts. There is a hierarchy of activities in human life: productive activity serves or is guided by the moral life; the moral life is guided by practical reason; practical reason (used in moral and political life) serves contemplative reason (whereby we contemplate God). Practical reason sets aside time and resources for contemplative reason. − + − + − <!-- This section is for direct examples of a hierarchical system ONLY, and only ones that have not been summarized above. Methodologies belong in the appropriate section below. Related concepts are listed under the "See also" section. If you are uncertain where a link belongs, place it in the "See also" section. HINT: If you can't easily say what it's a hierarchy OF, it doesn't belong here (but that doesn't imply that if you can say what its a hierarchy of, it belongs here). -->+ + − <！-- 本节仅供直接举例说明等级制度，仅供上文未概述的例子参考。方法学属于下面的适当部分。相关概念列在“请参阅”部分。如果您不确定链接属于哪个位置，请将其放在“请参阅”部分。提示: 如果你不能很容易地说出它是什么的层次结构，它就不属于这里(但这并不意味着只要你能说出它是什么的层次结构，它就属于这里)。-->+ + + − {{col-begin}}+ − {{col-3}}+ − ====Information-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "information-based hierarchies"-->+ − ====Information-based 基于信息====<!--yes, that hyphen IS correct, even per WP:HYPHEN—this category's logical title is "information-based hierarchies"-->+ − + − − * [[Library classification 图书馆分类法]] − − ** [[Dewey Decimal Classification 杜威十进制分类法]] − − {{col-3}} − − ====City planning-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "city planning-based hierarchies"--> − − ====City planning-based 基于城市规划====<!--yes, that hyphen IS correct, even per WP:HYPHEN—this category's logical title is "city planning-based hierarchies"--> − − = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = − − * [[Hierarchy of roads|Roads 道路]] − − ** [[Street hierarchy|Streets 街道]] − − * [[Settlement hierarchy 聚落等级]] − − ** [[Settlement hierarchy#Example of a settlement hierarchy|As of 2010 截至2010年]] − − ** [[Ekistic units|As of 2100 (estimate according to Doxiadis, 1968) 截至2010年（根据Doxiadis 1968年的估计）]] − − {{col-3}} − − − − ====Linguistics-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "linguistics-based hierarchies"--> − − ====Linguistics-based 基于语言学====<!--yes, that hyphen IS correct, even per WP:HYPHEN—this category's logical title is "linguistics-based hierarchies"--> − − = = = 基于语言学的 = = = = = < ! -- 是的，连字符是正确的，即使按 wp: hyphen ー这个类别的逻辑标题是“基于语言学的层次” -- > 第667行：
第318行： − {{col-end}} − − − − {{col-begin}} − − {{col-3}} − − − − ====Power- or authority-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "power- or authority-based hierarchies"--> − − ====Power- or authority-based 基于权利或权威====<!--yes, that hyphen IS correct, even per WP:HYPHEN—this category's logical title is "power- or authority-based hierarchies"--> − − = = = 权力-或基于权威 = = = = = < ! -- 是的，连字符是正确的，即使按照 wp: hyphen ー这个类别的逻辑标题是“权力-或基于权威的层次结构” -- > + 第747行：
第384行： − {{col-3}}+ − − − − − − ====Value-based 基于价值====<!--value meaning both money and relative importance--><!--yes, that hyphen IS correct, even per WP:HYPHEN—this category's logical title is "value-based hierarchies"--> − − = = = = = 基于价值的价值 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 第769行：
第398行： − {{col-3}}+ − − − − − − ====Perception-based 基于感知====<!--yes, that hyphen IS correct, even per WP:HYPHEN—this category's logical title is "perception-based hierarchies"--> − − = = = 基于感知的感知 = = = = = < ! -- 是的，连字符是正确的，即使按照 wp: hyphen ー这个类别的逻辑标题是“基于感知的层级” -- > 第786行：
第407行： − − {{col-end}} − {{col-begin}}+ − − {{col-3}} − − − − − − ====History-based 基于历史====<!--yes, that hyphen IS correct, even per WP:HYPHEN—this category's logical title is "history-based hierarchies"--> − − = = = 历史为基础 = = = = < ! -- 是的，连字符是正确的，即使按 wp: hyphen ー这个类别的逻辑标题是“基于历史的层级” -- > − 第815行：
第423行： − {{col-3}}+ − − − − − − <!--[[WP:HYPHEN]]—this category's logical title is "science-based hierarchies"--> − − <!--WP:HYPHEN—this category's logical title is "science-based hierarchies"--> − − < ! -- wp: hyphen ー这个类别的逻辑标题是"科学层次"> 第841行：
第439行： − − − {{col-3}} − + 第891行：
第486行： − + + − ====Religion-based 基于宗教====<!--yes, that hyphen IS correct, even per WP:HYPHEN—this category's logical title is "religion- and mythology-based hierarchies"-->+ − + 第964行：
第560行： + − ===Methods using hierarchy===<!-- See note at "Further applications"-->+ − ===Methods using hierarchy 使用层次结构的方法===<!-- See note at "Further applications"-->+ − = = = = 使用层次结构的方法 = = = < ! -- 参见“ further applications” -- > + 第1,020行：
第617行： − + − − ==See also 参见==<!-- See note at "Further applications"--> − − = = 也见 = = < ! -- 参见“ further applications” -- > 第1,086行：
第679行： − + − − ''(For example, in {{section link|#Subtype}})'' − − (For example, in ) − − (例如，在 − + − + 第1,110行：
第697行： − + 第1,138行：
第725行： − + 第1,150行：
第737行： − {{Authority control}} − − − − [[Category:Hierarchy| ]] − − [[Category:Patterns]] − − Category:Patterns − − 分类: 模式 − − [[Category:Structure]] − − Category:Structure − − 类别: 结构 − − [[Category:Political culture]] − − Category:Political culture − − 类别: 政治文化 − + + + − <small>This page was moved from [[wikipedia:en:Hierarchy]]. Its edit history can be viewed at [[层次/edithistory]]</small></noinclude> − [[Category:待整理页面]]+
无编辑摘要
{{#seo:
|keywords=自相似性，共形对称，膨胀
|description=层次 hierarchy从古希腊语“大祭司的统治”和“神圣仪式的主持者”而来,是一组相互之间被表示成具有“之上”“之下”或“同级”关系的元素（对象、名称、值、类别等）。在哲学、数学、计算机科学、系统论和社会科学（尤其是政治哲学）中，层次都是很重要的概念。
}}
'''<font color="#ff8000">“层次 hierarchy”</font>'''（从古希腊语 ἱεραρχία hierarkhia“大祭司的统治”和hierarkhes“神圣仪式的主持者”而来）是一组相互之间被表示成具有“之上”“之下”或“同级”关系的元素（对象、名称、值、类别等）。在哲学、数学、计算机科学、系统论和社会科学（尤其是政治哲学）中，层次都是很重要的概念。
'''<font color="#ff8000">“层次 hierarchy”</font>'''（从古希腊语 ἱεραρχία hierarkhia“大祭司的统治”和hierarkhes“神圣仪式的主持者”而来）是一组相互之间被表示成具有“之上”“之下”或“同级”关系的元素（对象、名称、值、类别等）。在哲学、数学、计算机科学、系统论和社会科学（尤其是政治哲学）中，层次都是很重要的概念。
==名称 Nomenclature==
==名称 Nomenclature==
层次结构有其特殊词汇，这些术语在层次图解（见下）中较易理解。
层次结构有其特殊词汇，这些术语在层次图解（见下）中较易理解。
在组织的语境下，以下术语的使用经常与层次结构相关:<ref name="Dawkins"/><ref name="Architecture"/>
在组织的语境下，以下术语的使用经常与层次结构相关:<ref name="Dawkins"/><ref name="Architecture"/>
*'''<font color="#ff8000">对象 Object</font>'''：一个实体（例如一个人，一个部门或概念或配置集中的一个元素或一组中的成员）
*'''<font color="#ff8000">对象 Object</font>'''：一个实体（例如一个人，一个部门或概念或配置集中的一个元素或一组中的成员）
*'''<font color="#ff8000">系统 System</font>'''：层次性地组织起来的一整组对象（例如管理体系）
*'''<font color="#ff8000">系统 System</font>'''：层次性地组织起来的一整组对象（例如管理体系）
*'''<font color="#ff8000">维度 Dimension</font>'''：联机分析处理（例如立方体）中“系统”的另一种说法
*'''<font color="#ff8000">维度 Dimension</font>'''：联机分析处理（例如立方体）中“系统”的另一种说法
*'''<font color="#ff8000">成员 Member</font>'''：处于（分类系统、分类学或维度）中任一（等级或阶层）的一个（元素或对象）
*'''<font color="#ff8000">成员 Member</font>'''：处于（分类系统、分类学或维度）中任一（等级或阶层）的一个（元素或对象）
*'''位置相关的术语 Terms about Positioning'''
*'''位置相关的术语 Terms about Positioning'''
**'''<font color="#ff8000">阶层 Rank</font>'''：一个对象的相对值、价值、复杂度、力量、重要度、权威性、等级等
**'''<font color="#ff8000">阶层 Rank</font>'''：一个对象的相对值、价值、复杂度、力量、重要度、权威性、等级等
**'''<font color="#ff8000">等级 Level</font>'''：阶层或重要度相同的一组对象
**'''<font color="#ff8000">等级 Level</font>'''：阶层或重要度相同的一组对象
**'''<font color="#ff8000">排序 Ordering</font>'''：等级或阶层的配置
**'''<font color="#ff8000">排序 Ordering</font>'''：等级或阶层的配置
**'''<font color="#ff8000">层次 Hierarchy</font>'''：将特定的一组成员按等级或阶层配置起来的组织。通过忽视所选等级以扁平化结构，一个维度、分类学或体系分类的多层次是可能的
**'''<font color="#ff8000">层次 Hierarchy</font>'''：将特定的一组成员按等级或阶层配置起来的组织。通过忽视所选等级以扁平化结构，一个维度、分类学或体系分类的多层次是可能的
*'''位置相关的术语Terms about Placement'''
*'''位置相关的术语Terms about Placement'''
**'''<font color="#ff8000">顶 Hierarch</font>'''：层次的顶，由位于维度中顶层的一个独立个体（对象或成员）组成。倒树形结构的根源
**'''<font color="#ff8000">顶 Hierarch</font>'''：层次的顶，由位于维度中顶层的一个独立个体（对象或成员）组成。倒树形结构的根源
**'''<font color="#ff8000">成员 Member</font>'''：维系（上级或下级）成员的维度中层次结构里任一层的一个成员或节点
**'''<font color="#ff8000">成员 Member</font>'''：维系（上级或下级）成员的维度中层次结构里任一层的一个成员或节点
**'''<font color="#ff8000">孤体 Orphan</font>'''：一个维度中某等级中的一没有父级的成员。通常是孤立分支的顶。孤体可通过创建与直接上层中的一个父级的关系而重新嫁接到层次中。
**'''<font color="#ff8000">孤体 Orphan</font>'''：一个维度中某等级中的一没有父级的成员。通常是孤立分支的顶。孤体可通过创建与直接上层中的一个父级的关系而重新嫁接到层次中。
**'''<font color="#ff8000">叶 Leaf</font>'''：维度中任一层里没有下级的成员
**'''<font color="#ff8000">叶 Leaf</font>'''：维度中任一层里没有下级的成员
**'''<font color="#ff8000">近邻 Neighbour</font>'''：同一等级或阶层中相邻与另一成员的成员，通常是同级。
**'''<font color="#ff8000">近邻 Neighbour</font>'''：同一等级或阶层中相邻与另一成员的成员，通常是同级。
**'''<font color="#ff8000">上级 Superior</font>'''：更高等级或更高等级中的对象（父级或祖先级）
**'''<font color="#ff8000">上级 Superior</font>'''：更高等级或更高等级中的对象（父级或祖先级）
**'''<font color="#ff8000">下级 Subordinate</font>'''：更低等级或更低等级中的对象（子级或后裔级）
**'''<font color="#ff8000">下级 Subordinate</font>'''：更低等级或更低等级中的对象（子级或后裔级）
**'''<font color="#ff8000">群 Collection</font>'''：一等级中的所有对象（例如同级成员）
**'''<font color="#ff8000">群 Collection</font>'''：一等级中的所有对象（例如同级成员）
**'''<font color="#ff8000">同级 Peer</font>'''：同一阶层（即同一等级）的对象
**'''<font color="#ff8000">同级 Peer</font>'''：同一阶层（即同一等级）的对象
**'''<font color="#ff8000">交互 Interaction</font>'''：对象与其直接上级或下级的关系（例如一对上下级）
**'''<font color="#ff8000">交互 Interaction</font>'''：对象与其直接上级或下级的关系（例如一对上下级）
***，一个对象比另一个刚好高一等级或低一等级时（例如在树形图中两个对象间有连线）发生'''<font color="#ff8000">直接 Direct</font>'''交互
***，一个对象比另一个刚好高一等级或低一等级时（例如在树形图中两个对象间有连线）发生'''<font color="#ff8000">直接 Direct</font>'''交互
**'''<font color="#ff8000">距离 Distance</font>'''：两个对象间的最小连接数，例如若连接数比对象数少1则需要一个对象到另一个对象的路径交叉
**'''<font color="#ff8000">距离 Distance</font>'''：两个对象间的最小连接数，例如若连接数比对象数少1则需要一个对象到另一个对象的路径交叉
**'''<font color="#ff8000">跨度 Span</font>'''：层级宽度图表化的量化表述，例如一个对象所拥有的下级的数量。
**'''<font color="#ff8000">跨度 Span</font>'''：层级宽度图表化的量化表述，例如一个对象所拥有的下级的数量。
*'''与自然相关的术语 Terms about Nature'''
*'''与自然相关的术语 Terms about Nature'''
**'''<font color="#ff8000">属性 Attribute</font>'''：等级中（成员或其下级）的遗传特征（例如''发色''）
**'''<font color="#ff8000">属性 Attribute</font>'''：等级中（成员或其下级）的遗传特征（例如''发色''）
**'''<font color="#ff8000">属性值 Attribute-value</font>'''：遗传特征的具体值（例如''棕发''）
**'''<font color="#ff8000">属性值 Attribute-value</font>'''：遗传特征的具体值（例如''棕发''）
在数学语境下（图论）所用的一般术语则不同。
在数学语境下（图论）所用的一般术语则不同。
===支化度 Degree of branching <span id="Terminology"></span>===
===支化度 Degree of branching===
支化度是指对象所有直接下级或子项的数量（在图论中，即有向图通过外向弧所连接的顶点数）。层次可按其“最大度”分类，即系统整体中存在的支化度的最高值，这种分类方式产生了两个广类：线性和支化。
支化度是指对象所有直接下级或子项的数量（在图论中，即有向图通过外向弧所连接的顶点数）。层次可按其“最大度”分类，即系统整体中存在的支化度的最高值，这种分类方式产生了两个广类：线性和支化。
'''<font color="#ff8000">线性层次结构</font>'''的最大度是1。<ref name="Dawkins"/>即所有对象都可呈现在一个列表中，每个对象(顶部和底部的除外)只有一个直接下级和一个直接上级。注意，这里说的是对象而不是级别；就级别而言每个层次结构都有这种属性，但每个级别通常可以有无限个对象。生命层次结构就是线性层次的一个例子。
'''<font color="#ff8000">线性层次结构</font>'''的最大度是1。即所有对象都可呈现在一个列表中，每个对象(顶部和底部的除外)只有一个直接下级和一个直接上级。注意，这里说的是对象而不是级别；就级别而言每个层次结构都有这种属性，但每个级别通常可以有无限个对象。生命层次结构就是线性层次的一个例子。
在'''<font color="#ff8000">分支层次结构</font>'''中，至少有一个对象的支化度在2或以上（即支化度下限是2或更高）。<ref name="Dawkins"/> 对许多人来说，提到“层次”这个词就会想起支化层次结构。<ref name="Dawkins"/> 支化层次存在于很多系统中，包括组织、分类法。广义上的分支层次可据其分支度进一步细分。
在'''<font color="#ff8000">分支层次结构</font>'''中，至少有一个对象的支化度在2或以上（即支化度下限是2或更高）。<ref name="Dawkins"/> 对许多人来说，提到“层次”这个词就会想起支化层次结构。<ref name="Dawkins"/> 支化层次存在于很多系统中，包括组织、分类法。广义上的分支层次可据其分支度进一步细分。
'''<font color="#ff8000">扁平层次结构</font>'''是指最大度接近无穷的支化层次结构，例如跨度很大的层次结构。<ref name="Architecture">{{cite journal|last=Simon|first=Herbert A.|title=The Architecture of Complexity|journal=[[Proc. Am. Philos. Soc.]]|volume=106|issue=6|date=12 December 1962|pages=467–482|publisher=[[American Philosophical Society]]|issn=0003-049X|location=Philadelphia, Pennsylvania |jstor=985254 |citeseerx=10.1.1.110.961}}{{registration required}}</ref>分层系统一般最多只有中等的跨度，故扁平层次结构通常根本不被视为层次结构。例如钻石和石墨是由许多碳原子组成的扁平层次结构，而这些碳原子可进一步分解为亚原子粒子。
'''<font color="#ff8000">扁平层次结构</font>'''是指最大度接近无穷的支化层次结构，例如跨度很大的层次结构。<ref name="Architecture">{{cite journal|last=Simon|first=Herbert A.|title=The Architecture of Complexity|journal=[[Proc. Am. Philos. Soc.]]|volume=106|issue=6|date=12 December 1962|pages=467–482|publisher=[[American Philosophical Society]]|issn=0003-049X|location=Philadelphia, Pennsylvania |jstor=985254 |citeseerx=10.1.1.110.961}}{{registration required}}</ref>分层系统一般最多只有中等的跨度，故扁平层次结构通常根本不被视为层次结构。例如钻石和石墨是由许多碳原子组成的扁平层次结构，而这些碳原子可进一步分解为亚原子粒子。
'''<font color="#ff8000">重叠层次结构</font>'''是指至少有一个对象具有两个父级对象的分支层次结构。<ref name="Dawkins"/>例如，一个研究生可以有两个联合主管，学生可同等地直接向他们汇报，且二人在大学层级制度中具有同等的权力水平(例如他们都拥有相同的职位或任期)。
'''<font color="#ff8000">重叠层次结构</font>'''是指至少有一个对象具有两个父级对象的分支层次结构。<ref name="Dawkins"/>例如，一个研究生可以有两个联合主管，学生可同等地直接向他们汇报，且二人在大学层级制度中具有同等的权力水平(例如他们都拥有相同的职位或任期)。
==术语历史 History of the term==
==术语历史 History of the term==
“层次”这一英语单词的首次被牛津英语词典引用的使用可能是在1881年，被用来指伪狄奥尼修斯 Pseudo-Dionysius the Areopagite（5-6世纪）所描述的3个天使的3个阶层。伪狄奥尼修斯使用相关的希腊单词(ἱεραρχία hierarchia) 来指代天界阶层和教会阶层。<ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy<!-- Bot generated title -->]</ref> 希腊语 ἱεραρχία表示大祭司的统治<ref>[https://www.etymonline.com/word/hierarchy "hierarchy"]. [[Online Etymology Dictionary]].</ref>（源自ἱεράρχης hierarches，“神圣仪式的主持，高阶祭司”，自ἱερεύς hiereus, “祭司”<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28ereu%2Fs ἱερεύς], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>，及 ἀρχή arche等“最初的地方或力量，统治”<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Da%29rxh%2F ἀρχή], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>）
“层次”这一英语单词的首次被牛津英语词典引用的使用可能是在1881年，被用来指伪狄奥尼修斯 Pseudo-Dionysius the Areopagite（5-6世纪）所描述的3个天使的3个阶层。伪狄奥尼修斯使用相关的希腊单词(ἱεραρχία hierarchia) 来指代天界阶层和教会阶层。<ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy<!-- Bot generated title -->]</ref> 希腊语 ἱεραρχία表示大祭司的统治<ref>[https://www.etymonline.com/word/hierarchy "hierarchy"]. [[Online Etymology Dictionary]].</ref>（源自ἱεράρχης hierarches，“神圣仪式的主持，高阶祭司”，自ἱερεύς hiereus, “祭司”<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28ereu%2Fs ἱερεύς], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>，及 ἀρχή arche等“最初的地方或力量，统治”<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Da%29rxh%2F ἀρχή], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>）
伪狄奥尼修斯首次将其用作抽象名词概念，自阶层式教会，如罗马天主教和东正教，拥有现代语义上的层次性结构（按照传统层次结构的顶部或头部表示神）以来，该术语开始指称世俗语境下类似的组织方式。
伪狄奥尼修斯首次将其用作抽象名词概念，自阶层式教会，如罗马天主教和东正教，拥有现代语义上的层次性结构（按照传统层次结构的顶部或头部表示神）以来，该术语开始指称世俗语境下类似的组织方式。
==层次的视觉呈现 Visually representing hierarchies==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->
==层次的视觉呈现 Visually representing hierarchies==
[[File:Maslow's hierarchy of needs.png|thumb|right|200px|[[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]]. This is an example of a hierarchy visualized with a triangle diagram.]]
[[File:Maslow's hierarchy of needs.png|thumb|right|200px|[[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]]. This is an example of a hierarchy visualized with a triangle diagram.]]
'''<font color="#ff8000">马斯洛的人类需求层次理论 Maslow's hierarchy of human needs</font>'''这是用三角图表呈现层次结构的一个实例。
'''<font color="#ff8000">马斯洛的人类需求层次理论 Maslow's hierarchy of human needs</font>'''这是用三角图表呈现层次结构的一个实例。
层次结构通常被描述为金字塔形，其中高度代表层次状态而宽度代表该层的元素多寡。<ref>{{cite book | title=Regions of War and Peace | publisher=University of Cambridge | author=Douglas Lemke | year=2002 | location=Cambridge | pages=49}}</ref>例如，一个公司的几个董事处于顶峰，而基层可能是成千上万没有下级的人。
这样的金字塔通常用树形或三角形图表绘制（注意，并非所有的三角形/金字塔形图表都是层次性的；例如1992年美国农业部膳食指南金字塔），两种图表都表现了各层次的大小差异。右侧是一个三角形图表的例子。组织结构图是组织内部层次结构的图表，在下面的树形图中有所描述。
这样的金字塔通常用树形或三角形图表绘制（注意，并非所有的三角形/金字塔形图表都是层次性的；例如1992年美国农业部膳食指南金字塔），两种图表都表现了各层次的大小差异。右侧是一个三角形图表的例子。组织结构图是组织内部层次结构的图表，在下面的树形图中有所描述。
最近，随着计算机的发展使存储和索引更大的数据集成为可能，人们开发出各种能更有效地利用计算机屏幕空间的方法来表示层次结构。例如分形图、树形图和辐射状树图。
最近，随着计算机的发展使存储和索引更大的数据集成为可能，人们开发出各种能更有效地利用计算机屏幕空间的方法来表示层次结构。例如分形图、树形图和辐射状树图。
==视觉层次 Visual hierarchy==
==视觉层次 Visual hierarchy==
在设计领域，主要是平面设计，文件内容排版和格式的成功很大程度上取决于视觉层次的规则。视觉层次对于像样的电脑文件的安配也至关重要。
在设计领域，主要是平面设计，文件内容排版和格式的成功很大程度上取决于视觉层次的规则。视觉层次对于像样的电脑文件的安配也至关重要。
嵌套集群是层次结构的一个可视化示例。嵌套集群用信息层来表示层次关系。子元素位于父元素之内，例如'''<font color="#ff8000">维恩图 Venn diagram</font>'''。这种结构可有效表示简单层次关系。例如，当需要打开一个电脑桌面的文件时，可能要先让操作者打开主文件夹，然后是主文件夹中的子文件夹，不断打开直到找到指定文件。
嵌套集群是层次结构的一个可视化示例。嵌套集群用信息层来表示层次关系。子元素位于父元素之内，例如'''<font color="#ff8000">维恩图 Venn diagram</font>'''。这种结构可有效表示简单层次关系。例如，当需要打开一个电脑桌面的文件时，可能要先让操作者打开主文件夹，然后是主文件夹中的子文件夹，不断打开直到找到指定文件。
对于更复杂的层次结构，楼梯结构用堆叠效果表示层次关系。请从视觉上想象一下从左到右下楼楼梯的顶部，子元素位于楼梯底部而父元素位于顶部。当表示更复杂的层次结构时，这种结构非常有效，尤其当台阶没有位于明显的序列中时。下一台阶必须基于所有台阶都顺序显示后才会出现。在计算机桌面的例子中，只有先打开别的文件才能找到目标文件，因为通向目标文件的链接位于另一个文件内。所有步骤都必须完成才能到达最终目标。
对于更复杂的层次结构，楼梯结构用堆叠效果表示层次关系。请从视觉上想象一下从左到右下楼楼梯的顶部，子元素位于楼梯底部而父元素位于顶部。当表示更复杂的层次结构时，这种结构非常有效，尤其当台阶没有位于明显的序列中时。下一台阶必须基于所有台阶都顺序显示后才会出现。在计算机桌面的例子中，只有先打开别的文件才能找到目标文件，因为通向目标文件的链接位于另一个文件内。所有步骤都必须完成才能到达最终目标。
==通俗表达 Informal representation==
==通俗表达 Informal representation==
在日常英语中，层次可以被看作是一个集合，其中:<ref name="Dawkins">{{cite conference|last=Dawkins|first=Richard|authorlink=Richard Dawkins|title=Hierarchical organization: a candidate principle for ethology|conference=Growing points in ethology: based on a conference sponsored by St. John's College and King's College, Cambridge|editor1=Bateson, Paul Patrick Gordon |editor2=Hinde, Robert A.|year=1976|publisher=Cambridge University Press|location=Cambridge, England|isbn=0-521-29086-4|pages=7–54}}</ref>
# 任何元素都不高于自身，且
# 任何元素都不高于自身，且
# 其中有一个''教主''元素，高于集合中的所有其他元素。
# 其中有一个''教主''元素，高于集合中的所有其他元素。
第一个前提也可理解为层次结构不能有循环关系; 两个对象之间的关联总是可传递的。
第一个前提也可理解为层次结构不能有循环关系; 两个对象之间的关联总是可传递的。
第二个要求则确定了层次结构必须有一个所有元素都共有的代表或根源。
第二个要求则确定了层次结构必须有一个所有元素都共有的代表或根源。
==数学表达 Mathematical representation==
==数学表达 Mathematical representation==
==亚型 Subtypes==
==亚型 Subtypes==
===嵌套层次 Nested hierarchy===<!--if you change this title, change the wiki links within the article that link to it!-->
===嵌套层次 Nested hierarchy===
[[File:Russian-Matroshka no bg.jpg|200px|right|thumb|
'''玛特罗什卡套娃 Matryoshka Doll'''，又称嵌套娃娃或俄罗斯套娃。每个洋娃娃都被包裹在另一个洋娃娃里面，直到最小的洋娃娃。这就是嵌套的概念。当这个概念应用于集合时，其结果排序是一个嵌套的层次结构。]]
嵌套层次结构或包含层次结构，是指嵌套集的层次结构排序。<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref>嵌套的概念在俄罗斯套娃中得到体现。每个玩偶都被另一个玩偶包裹着，一直到最外层的。外部的套娃包含所有其内部的玩偶，往外一层的玩偶也包含所有其内部剩余的玩偶，如此反复。套娃结构是一个每层都只有一个对象的嵌套层次结构，例如在套娃中同样大小的玩偶只有一个；广义的嵌套层次可以每层都有多个对象，但每层里的对象都只有一个父级对象。嵌套层次一般概念的论证及数学表达如下：
: <math> \text{square} \subset \text{quadrilateral} \subset \text{polygon} \subset \text{shape} \, </math>
: <math> \text{square} \subset \text{quadrilateral} \subset \text{polygon} \subset \text{shape} \, </math>
正方形总是可以被称为四边形、多边形或形状。这样看来是层次性的。然而若多边形集采用这种分类法，则正方形只能是四边形，而不会是三角形、六边形等。
正方形总是可以被称为四边形、多边形或形状。这样看来是层次性的。然而若多边形集采用这种分类法，则正方形只能是四边形，而不会是三角形、六边形等。
嵌套层次结构是'''<font color="#ff8000">分类学 Taxonomies</font>''' 和'''<font color="#ff8000">系统分类 Systematic Classifications</font>'''背后的组织性方案。例如，在最初的'''<font color="#ff8000">林奈分类法 Linnaean Taxonomy</font>'''（他在《自然系统》第10版中所列）中，人类可被归为：ref>{{cite book|title=Systema naturae per regna tria naturae :secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis|last=Linnaei|first=Carl von|authorlink=Carl Linnaeus|year=1959|edition=10th|language=Latin|url=https://www.biodiversitylibrary.org/bibliography/542#|location=[[Stockholm]]|publisher=Impensis Direct|isbn=0-665-53008-0|accessdate=2011-09-24}}</ref>
嵌套层次结构是'''<font color="#ff8000">分类学 Taxonomies</font>''' 和'''<font color="#ff8000">系统分类 Systematic Classifications</font>'''背后的组织性方案。例如，在最初的'''<font color="#ff8000">林奈分类法 Linnaean Taxonomy</font>'''（他在《自然系统》第10版中所列）中，人类可被归为：ref>{{cite book|title=Systema naturae per regna tria naturae :secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis|last=Linnaei|first=Carl von|authorlink=Carl Linnaeus|year=1959|edition=10th|language=Latin|url=https://www.biodiversitylibrary.org/bibliography/542#|location=[[Stockholm]]|publisher=Impensis Direct|isbn=0-665-53008-0|accessdate=2011-09-24}}</ref>
: <math>\text{H. sapiens} \subset \text{Homo} \subset \text{Primates} \subset \text{Mammalia} \subset \text{Animalia}</math>
: <math>\text{H. sapiens} \subset \text{Homo} \subset \text{Primates} \subset \text{Mammalia} \subset \text{Animalia}</math>
'''<font color="#ff8000">分类法 Taxonomies</font>'''可能会频繁改变（如在生物分类法中所见），但嵌套层次结构这一基本理念始终不变。
'''<font color="#ff8000">分类法 Taxonomies</font>'''可能会频繁改变（如在生物分类法中所见），但嵌套层次结构这一基本理念始终不变。
在许多编程分类法和句法模型（以及数学中的分形）中，嵌套的层次结构，包括俄罗斯套娃，也用作自相似和递归性质的呈现。递归本身是层次性编程的一个子集，递归思维可用作层次思维和逻辑的同义词。<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref>
在许多编程分类法和句法模型（以及数学中的分形）中，嵌套的层次结构，包括俄罗斯套娃，也用作自相似和递归性质的呈现。递归本身是层次性编程的一个子集，递归思维可用作层次思维和逻辑的同义词。<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref>
===包容层次 Containment hierarchy===
===包容层次 Containment hierarchy===
包容层次是嵌套层次概念的直接外推。所有的有序集仍然是嵌套的，但是每个集合必须是“严格”的——不存在两个相同的集合。上面的图形示例可稍作改变来对此进行论证:
包容层次是嵌套层次概念的直接外推。所有的有序集仍然是嵌套的，但是每个集合必须是“严格”的——不存在两个相同的集合。上面的图形示例可稍作改变来对此进行论证:
: <math> \text{square} \subsetneq \text{quadrilateral} \subsetneq \text{polygon} \subsetneq \text{shape} \, </math>
: <math> \text{square} \subsetneq \text{quadrilateral} \subsetneq \text{polygon} \subsetneq \text{shape} \, </math>
符号 < math > x subsetneq y，</math > 表示x是y的子集，但不等于y。
符号 < math > x subsetneq y，</math > 表示x是y的子集，但不等于y。
包容层次有包含包容层次和组合包容层次两种。包含包容层次“包含”其子级，而组合包容层次“组合”其子级。层次结构也可能同时是包含的和组合的。<ref name="AI industrial">{{cite encyclopedia|title=Industrial and Engineering Applications of Artificial Intelligence and Expert Systems|last=Kopisch|first=Manfred|last2=Günther|first2=Andreas|doi=10.1007/BFb0024994|editor-last=Belli|editor-first=Fevzi|encyclopedia=Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings|year=1992|publisher=[[Springer Science+Business Media|Springer]]|pages=424–427|isbn=3-540-55601-X|series=Lecture Notes in Computer Science Series|volume=602|issn=0302-9743|editor6-last=Radermacher|editor8-first=Franz-Josef|chapter=Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control}}</ref>
包容层次有包含包容层次和组合包容层次两种。包含包容层次“包含”其子级，而组合包容层次“组合”其子级。层次结构也可能同时是包含的和组合的。<ref name="AI industrial">{{cite encyclopedia|title=Industrial and Engineering Applications of Artificial Intelligence and Expert Systems|last=Kopisch|first=Manfred|last2=Günther|first2=Andreas|doi=10.1007/BFb0024994|editor-last=Belli|editor-first=Fevzi|encyclopedia=Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings|year=1992|publisher=[[Springer Science+Business Media|Springer]]|pages=424–427|isbn=3-540-55601-X|series=Lecture Notes in Computer Science Series|volume=602|issn=0302-9743|editor6-last=Radermacher|editor8-first=Franz-Josef|chapter=Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control}}</ref>
=====包容层次结构 Subsumptive containment hierarchy=====
=====包容层次结构 Subsumptive containment hierarchy=====
<font color="#32CD32">包容层次结构 subsumptive containment hierarchy</font>是对象类从一般到特定的分类。这类层次结构的其他名称是“分类层次结构”和“ IS-A 层次结构”。最后一个术语描述了每个级别之间的关系——较低级别的对象“是”较高级别类的成员。上面概述的分类结构是一个包容性的层次结构。再次使用林奈分类系统的例子，可以看到，属于<font color="#ff8000">哺乳动物 Mammalia </font>等级的物体“是”动物等级的成员；更具体地说，人类“是”灵长类动物，灵长类动物“是”哺乳动物等等。也可以抽象地将包含的层次结构定义为“概念”的层次结构。例如，根据上述的林奈分类系统，像动物这样的实体名称是对所有符合动物概念的物种进行分类的一种方法。
<font color="#32CD32">包容层次结构 subsumptive containment hierarchy</font>是对象类从一般到特定的分类。这类层次结构的其他名称是“分类层次结构”和“ IS-A 层次结构”。<ref name="Lehmann"/><ref name="ibm">{{cite web|url=http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|archive-url=https://archive.today/20130103052727/http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|url-status=dead|archive-date=3 January 2013|title=Compositional hierarchy|work=WebSphere Transformation Extender Design Studio|accessdate=9 October 2009}}</ref><ref name="sys model">{{cite book|chapter=An advanced modeling environment based on a hybrid AI-OR approach|chapterurl=https://books.google.com/books?id=ds2eIQ6XZy0C&pg=PA366|pages=366–75|last=Funke|first=Birger|last2=Sebastian|first2=Hans-Jürgen|title=Systems modelling and optimization: proceedings of the 18th IFIP TC7 conference|volume=396|series=Research notes in mathematics series|editor1-last=Polis|editor1-first=Michael P.|editor2-last=Dontchev|editor2-first=Asen L.|editor3-last=Kall|editor3-first=Peter|editor4-last=Lascieka|editor4-first=Irena|editor5-last=Olbrot|editor5-first=Andrzej W.|publisher=[[CRC Press]]|year=1999|isbn=978-0-8493-0607-5}}</ref>最后一个术语描述了每个级别之间的关系——较低级别的对象“是”较高级别类的成员。上面概述的分类结构是一个包容性的层次结构。再次使用林奈分类系统的例子，可以看到，属于<font color="#ff8000">哺乳动物 Mammalia </font>等级的物体“是”动物等级的成员；更具体地说，人类“是”灵长类动物，灵长类动物“是”哺乳动物等等。也可以抽象地将包含的层次结构定义为“概念”的层次结构。例如<ref name="sys model"/>，根据上述的林奈分类系统，像动物这样的实体名称是对所有符合动物概念的物种进行分类的一种方法。
=====构成性包容层次结构 Compositional containment hierarchy=====
=====构成性包容层次结构 Compositional containment hierarchy=====
<font color="#32CD32">构成性包容层次结构 Compositional containment hierarchy</font>是构成系统的各个部分的顺序——系统是由这些部分“构成”的。<ref name="Parsons">{{cite book|last=Parsons|first=David|title=Object Oriented Programming in C++|publisher=Cengage Learning|year=2002|pages=110–185|isbn=0-8264-5428-3}}</ref>大多数工程结构，无论是自然的还是人工的，都可以用这种方式分解。
每个人每时每刻都会遇到的构成性层次就是<font color="#ff8000">生命的层次结构 hierarchy of life</font>。每个人都可以被分解为<font color="#ff8000">器官系统 organ system</font>，器官系统是由器官构成的，器官又是由组织构成的，组织是由细胞构成的，分子是由原子构成的。事实上，至少在宏观层面上，最后两个层次适用于所有物质。此外，每个级别都继承了它们子级别的所有属性。
每个人每时每刻都会遇到的构成性层次就是<font color="#ff8000">生命的层次结构 hierarchy of life</font>。每个人都可以被分解为<font color="#ff8000">器官系统 organ system</font>，器官系统是由器官构成的，器官又是由组织构成的，组织是由细胞构成的，分子是由原子构成的。事实上，至少在宏观层面上，最后两个层次适用于所有物质。此外，每个级别都继承了它们子级别的所有属性。
在这个特定的例子中，还有一些<font color="#ff8000">涌现特性 emergent properties</font>——在较低层次上看不到的功能（例如<font color="#ff8000">认知 cognition</font>不是神经元的特性，而是大脑的特性）——以及标度特性（分子比原子大，细胞比分子大等等）。这两个概念通常都存在于组合层次结构中，但它们不是必要的一般属性。这些层次结构是拥有属性的双向因果关系。涉及较低层次实体的<font color="#ff8000">上向因果关系 Upward causation</font>导致较高层次实体的某些属性；子实体可以相互作用产生父实体，并且父实体至少部分由他们的子实体组成。<font color="#ff8000">下向因果关系 Downward causation</font>是指将实体 x 并入更高级别的实体可能对 x 的属性和相互作用产生的影响。此外，每个级别上的实体都是<font color="#ff8000">自治的 autonomous</font>。
在这个特定的例子中，还有一些<font color="#ff8000">涌现特性 emergent properties</font>——在较低层次上看不到的功能（例如<font color="#ff8000">认知 cognition</font>不是神经元的特性，而是大脑的特性）——以及标度特性（分子比原子大，细胞比分子大等等）。这两个概念通常都存在于组合层次结构中，但它们不是必要的一般属性。这些层次结构是拥有属性的双向因果关系。涉及较低层次实体的<font color="#ff8000">上向因果关系 Upward causation</font>导致较高层次实体的某些属性；子实体可以相互作用产生父实体，并且父实体至少部分由他们的子实体组成。<font color="#ff8000">下向因果关系 Downward causation</font>是指将实体 x 并入更高级别的实体可能对 x 的属性和相互作用产生的影响。此外，每个级别上的实体都是<font color="#ff8000">自治的 autonomous</font>。
==Contexts and applications 语境和应用==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->
==Contexts and applications 语境和应用==
根据 Kulish v. v. (2002) 的研究，几乎世界上所有的组织系统都是等级制度的。<ref name="electrodynamics">{{cite book|title=Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics|last=Kulish|first=V. V.|isbn=1-4020-0757-4|year=2002|volume=1|publisher=[[Springer Science+Business Media|Springer]]|pages=xvii–xx; 49–71}}</ref>按照他们的共同定义，每个<font color="#ff8000">国家 nation</font>都有一个政府，每个政府都是层级制度的。<ref>{{Cite book|contribution=government|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/government?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref><ref>{{Cite book|contribution=nation|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/nation?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref> 社会经济系统被分为一个社会等级制（社会的<font color="#ff8000">社会分层 social stratification</font>） ，所有的系统分类方案(分类法)都是分等级的。大多数有组织的宗教，不管它们的内部管理结构如何，都在上帝之下按照层级运作。许多<font color="#ff8000">基督教教派 Christian denominations</font>都有一个独立的教会领导层次。从表亲关系（例如，第一代表兄弟，第二代表兄弟等等）、祖先(由<font color="#ff8000">家谱 family tree</font>描述)和继承(继承和继承权)的角度来看，家庭可以看作是一种等级结构。一个全面的生活和生活方式的所有必需品都可以用<font color="#ff8000">马斯洛人类需求层次 Maslow's hierarchy of human needs</font>来组织。学习通常必须遵循一个层次框架——学习微分方程必须先学习微积分；学习微积分必须先学习初等代数等等。甚至自然本身也有它自己的层级，许多方案试图记录下来，例如林奈分类学、生命的组织和生物量金字塔。层级制度是如此地深入到日常生活中，以至于人们认为它们微不足道。<ref name="Dawkins"/><ref name="electrodynamics"/>
根据 Kulish v. v. (2002) 的研究，几乎世界上所有的组织系统都是等级制度的。<ref name="electrodynamics">{{cite book|title=Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics|last=Kulish|first=V. V.|isbn=1-4020-0757-4|year=2002|volume=1|publisher=[[Springer Science+Business Media|Springer]]|pages=xvii–xx; 49–71}}</ref>按照他们的共同定义，每个<font color="#ff8000">国家 nation</font>都有一个政府，每个政府都是层级制度的。<ref>{{Cite book|contribution=government|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/government?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref><ref>{{Cite book|contribution=nation|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/nation?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref> 社会经济系统被分为一个社会等级制（社会的<font color="#ff8000">社会分层 social stratification</font>） ，所有的系统分类方案(分类法)都是分等级的。大多数有组织的宗教，不管它们的内部管理结构如何，都在上帝之下按照层级运作。许多<font color="#ff8000">基督教教派 Christian denominations</font>都有一个独立的教会领导层次。从表亲关系（例如，第一代表兄弟，第二代表兄弟等等）、祖先(由<font color="#ff8000">家谱 family tree</font>描述)和继承(继承和继承权)的角度来看，家庭可以看作是一种等级结构。一个全面的生活和生活方式的所有必需品都可以用<font color="#ff8000">马斯洛人类需求层次 Maslow's hierarchy of human needs</font>来组织。学习通常必须遵循一个层次框架——学习微分方程必须先学习微积分；学习微积分必须先学习初等代数等等。甚至自然本身也有它自己的层级，许多方案试图记录下来，例如林奈分类学、生命的组织和生物量金字塔。层级制度是如此地深入到日常生活中，以至于人们认为它们微不足道。<ref name="Dawkins"/><ref name="electrodynamics"/>
虽然上面的例子通常以层次形式清楚地描述并且很经典，但是层次结构也存在于许多分支结构并不是很明显的系统中。例如，大多数<font color="#ff8000">邮政编码 postal code</font>系统是分层的。以加拿大邮政编码系统为例，顶层的概念是“<font color="#ff8000">邮区 postal district</font>”，由18个对象(字母)组成。下一层是“<font color="#ff8000">地区 zone</font>”，其中的对象是数字0-9。这是重叠层次结构的一个例子，因为这10个对象中的每一个都有18个父对象。层次继续向下生成，理论上存在720万个 A0A 0A0 (第二个和第三个字母的位置每个允许20个对象)格式的唯一代码。大多数图书分类法系统也是分层级的。<font color="#ff8000">杜威十进制图书分类法 Dewey Decimal System</font>被认为是无限层次的，因为在小数点之后可以使用的数字数量是没有限制的。<ref name="Dewey">{{cite journal|title=Tracking Nuclear Sources|date=May–June 2009|last=Walker|first=Randy|publisher=wellservicingmagazine.com|pages=28–30|url=http://wellservicingmagazine.com/sites/default/files/pdfmag/WSM_MAYJUN09.PDF}}{{dead link|date=November 2017 |bot=InternetArchiveBot |fix-attempted=yes}} See also [[Dewey Decimal Classification|Wikipedia article]].</ref>
以树的形式描述的组织层次结构。这样的图被称为<font color="#ff8000">组织结构图 organizational charts</font>。
以树的形式描述的组织层次结构。这样的图被称为<font color="#ff8000">组织结构图 organizational charts</font>。
===Organizations 组织===
===Organizations 组织===
<font color="#ff8000">组织 Organizations</font>可以被构建成一个<font color="#32CD32">支配等级 dominance hierarchy</font>。在一个组织的层次结构中，有一个人或一个群体拥有最大的权力和权威，每个后续的层次代表一个较小的权威。大多数组织都是这样构建的，包括政府、公司、民兵和有组织的宗教。组织中的单位或人员在组织结构图中按等级进行描述。
<font color="#ff8000">组织 Organizations</font>可以被构建成一个<font color="#32CD32">支配等级 dominance hierarchy</font>。在一个组织的层次结构中，有一个人或一个群体拥有最大的权力和权威，每个后续的层次代表一个较小的权威。大多数组织都是这样构建的，包括政府、公司、民兵和有组织的宗教。组织中的单位或人员在组织结构图中按等级进行描述。
在<font color="#32CD32">反向层次结构 reverse hierarchy</font>中，权威的概念金字塔是颠倒的，因此顶点在底部，底部在顶部。这种模式代表了等级较高的成员对等级较低的成员负责的思想。
在<font color="#32CD32">反向层次结构 reverse hierarchy</font>中，权威的概念金字塔是颠倒的，因此顶点在底部，底部在顶部。这种模式代表了等级较高的成员对等级较低的成员负责的思想。
=== Life 生命===
=== Life 生命===
在实践中，我们观察到自然界中很大一部分(复杂的)生物系统呈现出层次结构。从理论上讲，在一个复杂性必须从简单性演化而来的世界中，我们可以预期复杂系统具有层次结构。20世纪50年代进行的系统层次分析，<ref>{{harvnb|Evans|1951}}</ref><ref>{{harvnb|Evans|1956}}</ref>为从20世纪80年代开始的层次生态学领域奠定了经验基础。<ref>{{harvnb|Margalef|1975}}</ref><ref>{{harvnb|O'Neill|1986}}</ref><ref>{{harvnb|Wicken|Ulanowicz|1988}}</ref><ref>{{harvnb|Pumain|2006}}</ref><ref>{{harvnb|Jordan|Jørgensen|2012}}</ref>
在实践中，我们观察到自然界中很大一部分(复杂的)生物系统呈现出层次结构。从理论上讲，在一个复杂性必须从简单性演化而来的世界中，我们可以预期复杂系统具有层次结构。20世纪50年代进行的系统层次分析，<ref>{{harvnb|Evans|1951}}</ref><ref>{{harvnb|Evans|1956}}</ref>为从20世纪80年代开始的层次生态学领域奠定了经验基础。<ref>{{harvnb|Margalef|1975}}</ref><ref>{{harvnb|O'Neill|1986}}</ref><ref>{{harvnb|Wicken|Ulanowicz|1988}}</ref><ref>{{harvnb|Pumain|2006}}</ref><ref>{{harvnb|Jordan|Jørgensen|2012}}</ref>
这些理论基础由热力学的方法来总结。当生物系统被模拟为物理系统时，在其最一般的抽象中，它们是表现出自组织行为的热力学开放系统，<font color="#ff8000">耗散结构 dissipative structures</font>之间的集合/子集关系可以用层次结构来刻画。
这些理论基础由热力学的方法来总结。当生物系统被模拟为物理系统时，在其最一般的抽象中，它们是表现出自组织行为的热力学开放系统，<font color="#ff8000">耗散结构 dissipative structures</font>之间的集合/子集关系可以用层次结构来刻画。
===Computer graphic imaging 计算机图形成像===
===Computer graphic imaging 计算机图形成像===
CGI 和<font color="#ff8000">计算机动画程序 computer animation programs</font>大多使用层次结构建模。例如在一个人体的三维模型中，胸部是左上臂的母体，而左上臂是左下臂的母体。层次结构用于几乎所有三维数字模型的建模和动画。
CGI 和<font color="#ff8000">计算机动画程序 computer animation programs</font>大多使用层次结构建模。例如在一个人体的三维模型中，胸部是左上臂的母体，而左上臂是左下臂的母体。层次结构用于几乎所有三维数字模型的建模和动画。
===Linguistics 语言学===
===语言学===
许多语法理论都包括层次结构，例如短语结构语法。
许多语法理论都包括层次结构，例如短语结构语法。
克里语(Cree)和马普敦根语(Mapudungun)等<font color="#32CD32">正动-反动语言 Direct–inverse languages</font>不是通过不同的主语和宾语标记来区分动词的主语和宾语，而是通过人的层级来区分。
克里语(Cree)和马普敦根语(Mapudungun)等<font color="#32CD32">正动-反动语言 Direct–inverse languages</font>不是通过不同的主语和宾语标记来区分动词的主语和宾语，而是通过人的层级来区分。
在这个系统中，三个人(或者阿尔冈昆诸语言中四个人)被放在显著的等级中。为了区分哪个是主语，哪个是宾语，如果宾语的级别高于主语，则使用反向标记。
在这个系统中，三个人(或者阿尔冈昆诸语言中四个人)被放在显著的等级中。为了区分哪个是主语，哪个是宾语，如果宾语的级别高于主语，则使用反向标记。
另一方面，语言包括多种非等级性的现象。例如，代词和它所指的名词短语之间的关系，通常以非等级的方式跨越语法界限。
另一方面，语言包括多种非等级性的现象。例如，代词和它所指的名词短语之间的关系，通常以非等级的方式跨越语法界限。
===Music 音乐===
===音乐===
音乐作品的结构通常是按层次来理解的（例如 Heinrich Schenker （1768-1835，见 Schenkerian 分析） ，以及 Fred Lerdahl 和语言学家 Ray Jackendoff 1985年的《<font color="#ff8000">调性音乐的生成理论 Generative Theory of Tonal Music</font>》）。一段乐曲中所有音符的总和被理解为一个包含所有音符的曲面，它可以简化为更加稀疏和更加基本的运动类型。在Schenker的理论中运作的结构层次包括前景层次，这在音乐乐谱的所有细节中都可以看到；中间层次，大致上是对位进行和主音的总结; 背景层次，即 Ursatz，这是调性音乐著作中仅有的几个共享的基本“远距离对位”结构之一。
音乐作品的结构通常是按层次来理解的（例如 Heinrich Schenker （1768-1835，见 Schenkerian 分析） ，以及 Fred Lerdahl 和语言学家 Ray Jackendoff 1985年的《<font color="#ff8000">调性音乐的生成理论 Generative Theory of Tonal Music</font>》）。一段乐曲中所有音符的总和被理解为一个包含所有音符的曲面，它可以简化为更加稀疏和更加基本的运动类型。在Schenker的理论中运作的结构层次包括前景层次，这在音乐乐谱的所有细节中都可以看到；中间层次，大致上是对位进行和主音的总结; 背景层次，即 Ursatz，这是调性音乐著作中仅有的几个共享的基本“远距离对位”结构之一。
<font color="#ff8000">调性音乐 tonal music</font>的<font color="#ff8000">音高 pitches</font>和形式是按等级组织的，所有音高的重要性来自于它们与<font color="#ff8000">主调 tonic key</font>的关系，其他调中的次要主题在主要主题的再现中被带回主调。苏珊·麦克拉里（Susan McClary）在她的《女性结局（(Feminine Endings）一书中将这一点在奏鸣曲式中具体地与女性主义的性别层次结构(见上文)联系起来，甚至指出，主要的主题通常以前被称为“阳性” ，而次要主题被称为“阴性”。
<font color="#ff8000">调性音乐 tonal music</font>的<font color="#ff8000">音高 pitches</font>和形式是按等级组织的，所有音高的重要性来自于它们与<font color="#ff8000">主调 tonic key</font>的关系，其他调中的次要主题在主要主题的再现中被带回主调。苏珊·麦克拉里（Susan McClary）在她的《女性结局（(Feminine Endings）一书中将这一点在奏鸣曲式中具体地与女性主义的性别层次结构(见上文)联系起来，甚至指出，主要的主题通常以前被称为“阳性” ，而次要主题被称为“阴性”。
==Criticisms of views, concerning distinctions of type and categories well as distinguishability 关于类型和范畴的区别以及区别性的观点的批判==
==关于类型和范畴的区别以及区别性的观点的批判==
在William James(1842-1910)、Michel Foucault (1926-1984)和Hayden White等不同理论家的著作中，提出了对等级认识论的重要批判。詹姆斯在他的著作“彻底经验主义 Radical Empiricism”中断言，明确类型和范畴的区分是科学推理的一个恒定但不成文的目标，因此当此目标实现时，就是宣告成功之时。但是，如果世界的各个方面以不同的方式组织起来，涉及到固有的和难以解决的模糊性，那么科学问题通常被认为是没有解决的。
在William James(1842-1910)、Michel Foucault (1926-1984)和Hayden White等不同理论家的著作中，提出了对等级认识论的重要批判。詹姆斯在他的著作“彻底经验主义 Radical Empiricism”中断言，明确类型和范畴的区分是科学推理的一个恒定但不成文的目标，因此当此目标实现时，就是宣告成功之时。但是，如果世界的各个方面以不同的方式组织起来，涉及到固有的和难以解决的模糊性，那么科学问题通常被认为是没有解决的。
17世纪左右，伦理学中的等级制度在西欧、西亚和北非出现。在这方面，术语层次是指它们从真实到非真实是如何区分的。<font color="#ff8000">女权主义者 Feminists、马克思主义者 Marxists、无政府主义者 anarchists、共产主义者 communists、批判理论家 critical theorists</font>以及其他人，他们对人类社会中普遍存在的等级制度，尤其是社会关系中的等级制度，都有不同的解释与批判。等级制度存在于社会的各个部分：企业、学校、家庭等等。这些关系通常被认为是必要的。存在于等级结构中的实体可以是动物、人类、植物等等。
17世纪左右，伦理学中的等级制度在西欧、西亚和北非出现。在这方面，术语层次是指它们从真实到非真实是如何区分的。<font color="#ff8000">女权主义者 Feminists、马克思主义者 Marxists、无政府主义者 anarchists、共产主义者 communists、批判理论家 critical theorists</font>以及其他人，他们对人类社会中普遍存在的等级制度，尤其是社会关系中的等级制度，都有不同的解释与批判。等级制度存在于社会的各个部分：企业、学校、家庭等等。这些关系通常被认为是必要的。存在于等级结构中的实体可以是动物、人类、植物等等。
===Ethics, behavioral psychology, philosophies of identity 伦理，行为心理学，同一哲学 philosophies of identity ===
===伦理，行为心理学，同一哲学===
[[File:Hierarchy Of Purposes.jpg|thumb|right|alt=|
职业目标可以用一个描述次要行动如何支持一个更大的目标的层次结构来图示。
职业目标可以用一个描述次要行动如何支持一个更大的目标的层次结构来图示。
]]
<font color="#ff8000">伦理学 ethics</font>中会列举各种<font color="#ff8000">美德 virtues</font>，并有时将其根据特定美德理论有层次地组织起来。
<font color="#ff8000">伦理学 ethics</font>中会列举各种<font color="#ff8000">美德 virtues</font>，并有时将其根据特定美德理论有层次地组织起来。
在一些随机的例子中，结构层次之间的“构成的”重要性是不对称的，因此整个层次组的小部分的意义依赖于它们在更大部分中的隶属关系。人类生活中的活动有一种层次：生产活动服务于或被道德生活所指导；道德生活被实践理性所指导；实践理性(用于道德和政治生活)服务于冥想理性(我们借以思考上帝)。实用理性为深思的理由留出时间和资源。
在一些随机的例子中，结构层次之间的“构成的”重要性是不对称的，因此整个层次组的小部分的意义依赖于它们在更大部分中的隶属关系。人类生活中的活动有一种层次：生产活动服务于或被道德生活所指导；道德生活被实践理性所指导；实践理性(用于道德和政治生活)服务于冥想理性(我们借以思考上帝)。实用理性为深思的理由留出时间和资源。
==Examples of other applications 其他应用的例子==
==其他应用的例子==
<!-- This section is for direct examples of a hierarchical system ONLY, and only ones that have not been summarized above. Methodologies belong in the appropriate section below. Related concepts are listed under the "See also" section. If you are uncertain where a link belongs, place it in the "See also" section. HINT: If you can't easily say what it's a hierarchy OF, it doesn't belong here (but that doesn't imply that if you can say what its a hierarchy of, it belongs here). -->
<！-- 本节仅供直接举例说明等级制度，仅供上文未概述的例子参考。方法学属于下面的适当部分。相关概念列在“参见”部分。如果您不确定链接属于哪个位置，请将其放在“参见”部分。提示: 如果你不能很容易地说出它是什么的层次结构，它就不属于这里(但这并不意味着只要你能说出它是什么的层次结构，它就属于这里)。-->
====基于信息====
* [[图书馆分类法]]
** [[杜威十进制分类法]]
====基于城市规划====
* 道路
** 街道
* 聚落等级
** 截至2010年
** 截至2010年（根据Doxiadis 1968年的估计）
= = = = = 信息为基础 = = = = < ! -- 是的，连字符是正确的，即使按照 wp: hyphen ー这个类别的逻辑标题是“信息为基础的层次结构” -- >
====基于语言学====
* [[Tree model|Language family tree 语言家谱]]
* [[Tree model|Language family tree 语言家谱]]
* [[Color terms#Basic color terms|Evolution of basic color terminology in languages 语言中基本颜色术语的演变]]
* [[Color terms#Basic color terms|Evolution of basic color terminology in languages 语言中基本颜色术语的演变]]
====基于权利或权威====
* [[Noble ranks|Aristocratic hierarchies 贵族等级]]
* [[Noble ranks|Aristocratic hierarchies 贵族等级]]
====基于价值====
====Value-based====<!--value meaning both money and relative importance--><!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "value-based hierarchies"-->
* [[Hierarchy of genres|Hierarchy of genres in art 艺术流派的等级]]
* [[Hierarchy of genres|Hierarchy of genres in art 艺术流派的等级]]
====基于感知====
====Perception-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "perception-based hierarchies"-->
* [[Color wheel 色环]]
* [[Color wheel 色环]]
**** [[Tertiary colors 三次色]]
**** [[Tertiary colors 三次色]]
====基于历史====
====History-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "history-based hierarchies"-->
* [[Three-age system 史前三时代分类系统]]
* [[Three-age system 史前三时代分类系统]]
====基于科学====
====Science-based 基于科学====
* [[Earth's location in the universe#Earth in the universe|Hierarchy of organization within the Universe 宇宙中的组织层次]]
* [[Earth's location in the universe#Earth in the universe|Hierarchy of organization within the Universe 宇宙中的组织层次]]
* [[Ecological land classification#Hierarchy of classification levels in ecology compared to other fields|Hierarchy of ecological georegions 生态地理等级]]
* [[Ecological land classification#Hierarchy of classification levels in ecology compared to other fields|Hierarchy of ecological georegions 生态地理等级]]
====Technology-based 基于技术====
====基于技术====
* [[Memory hierarchy 存储层次结构]]
* [[Memory hierarchy 存储层次结构]]
====Religion-based====<!--yes, that hyphen IS correct, even per [[WP:HYPHEN]]—this category's logical title is "religion- and mythology-based hierarchies"-->
====基于宗教====
{{columns-list|colwidth=22em|
{{columns-list|colwidth=22em|
= = = = 基于宗教的 = = = = = = = = = = 是的，连字符是正确的，即使按照 wp: hyphen ー这个类别的逻辑标题是“基于宗教和神话的等级制度” -- >
{ columns-list | colwidth = 22em |
* Levels of consciousness 意识层次
* Levels of consciousness 意识层次
* (organizational hierarchies are listed under 组织和层次列举于{{nowrap|"[[#Power- or authority-based|Power- or authority-based]]"}})<!--non-breaking spaces used for neatness at all resolutions-->
* (organizational hierarchies are listed under 组织和层次列举于{{nowrap|"[[#Power- or authority-based|Power- or authority-based]]"}})<!--non-breaking spaces used for neatness at all resolutions-->
}}
}}
}}
===使用层次结构的方法===
{{columns-list|colwidth=22em|
{{columns-list|colwidth=22em|
}}
}}
==See also==<!-- See note at "Further applications"-->
==参见==
{{columns-list|colwidth=22em|
{{columns-list|colwidth=22em|
===Strucure-related concepts 结构相关概念===
===结构相关概念===
* [[Is-a]]
* [[Is-a]]
** [[Hypernymy 上位关系]] (and [[supertype 超类型]])
** [[Hypernymy 上位关系]] ( [[supertype 超类型]])
** [[Hyponymy 下义关系]] (and [[subtype 亚类型]])
** [[Hyponymy 下义关系]] ([[subtype 亚类型]])
* [[Has-a]]
* [[Has-a]]
{{Reflist}}
{{Reflist}}
==Further reading==
==拓展阅读==
* {{cite book|first=Valerie|last=Ahl|first2=Timothy F. H.|last2=Allen|authorlink2=Timothy F. H. Allen|year=1996|title=Hierarchy Theory|location=New York|publisher=Columbia University Press|isbn=0-231-08481-1}}
* {{cite book|first=Valerie|last=Ahl|first2=Timothy F. H.|last2=Allen|authorlink2=Timothy F. H. Allen|year=1996|title=Hierarchy Theory|location=New York|publisher=Columbia University Press|isbn=0-231-08481-1}}
==External links==
==相关链接==
{{wikiquote}}
{{wikiquote}}
<noinclude>
<br/><br/><br/>
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