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第18行： − 层次结构可直接或间接地、竖向或对角地连接实体。大体上呈层次结构的系统尽管也可对替代层次作合并，层次结构中唯一的直接关系就是其直接上级或直接下级关系。层次联系可通过同向的多个联系汇成的路径向上或向下发展。层次结构中所有没有垂直相连的部分都可以通过水平路径（向上找到共同直接或间接上级再向下）相连。就像两个同事、同僚向共同上级汇报，但他们各自都有同等的相对权限。组织形式的存在对层次既是替代也是补充。异质结构也是这样一种形式。+ 第30行：
第30行： − 层次有其特殊词汇，这些术语在层次图解（见下）中较易理解。+ 第39行：
第39行： − 在组织性的语境下，以下术语经常用于层次性:+ + − + − + − + − + − + − + − + − + − + − + − + − + − + 第94行：
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第132行： − 大多数层次结构按其主体不同而适用更具体的词汇，但其背后的理念是相同的。例如，在数据结构中，对象称为节点，上级称为父级，下级称为子级。在商业环境中，上级是主管/老板，同级即同事。+ 第141行：
第142行： − 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，系统中支化度的最高值表示系统整体，这种分类方式分化出两个分野：线性和支化。+ 第147行：
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第174行： − + + − 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"<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. − Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library</ref> 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.+ − “层次”这一英语单词的首次使用可能是在1881年的牛津英语词典里，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个位阶。伪狄奥尼修斯使用有关的希腊词汇(ἱεραρχία hierarchia) 来指代天界位阶和教会位阶。希腊语 ἱεραρχία表示大祭司的统治（来自ἱερεύς hiereus, “祭司”及 ἀρχή arche等“最初的地方或力量，统治”所衍生出的 ἱεράρχης hierarches，“神圣仪式的主持，“高阶祭司”）。伪狄奥尼修斯首次将其用作抽象名词概念，自阶层式教堂以来，例如罗马天主教和东正教教堂都有着现代语义上的层次性结构（传统意义上层次结构的顶部或头部表示神），该术语在长期语境下用于指称类似的结构方式。+ + 第195行：
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第215行： − 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，人们开发出各种方法来表示层次结构，以便更有效地利用计算机屏幕空间。例如分形图、树形图和辐射状树图。+ 第223行：
第223行： − 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规则。视觉层次对于像样的电脑文件组织也至关重要。+ 第249行：
第249行： − − No element is superior to itself, and 第256行：
第254行： − One element, the hierarch, is superior to all of the other elements in the set.+ − − 第276行：
第272行： − + − − 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 − − 第304行：
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第315行： − + − 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。每个洋娃娃都被另一个洋娃娃包裹着，一直到最外层的。外部的洋娃娃包含所有其内部的洋娃娃，往外一层的洋娃娃也包含所有其内部剩余的洋娃娃，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洋娃娃只有一个；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：+ 第339行：
第331行： − 正方形可称为四边形、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。+ 第347行：
第339行： − + + − − <math>\text{H. sapiens} \subset \text{Homo} \subset \text{Primates} \subset \text{Mammalia} \subset \text{Animalia}</math> − 第363行：
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第361行： − 在许多编程分类法和句法模型（以及数学中的分形）中，包括俄罗斯娃娃，嵌套的层次结构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。+ 第379行：
第369行： − 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论证:+ − − − <math> \text{square} \subsetneq \text{quadrilateral} \subsetneq \text{polygon} \subsetneq \text{shape} \, </math> 第410行：
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第423行： − 每个人每时每刻都会遇到的组合层次就是<font color="#ff8000">生命的层次 hierarchy of life</font>。每个人都可以归结为<font color="#ff8000">器官系统 organ system</font>，器官系统是由组织构成的，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，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。+ 第453行：
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第517行： − 许多语法理论都涉及层次，例如短语结构语法。+ 第551行：
第541行： − 另一方面，语言包括多种不分等级的现象。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。+ 第559行：
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第565行： − 在威廉·詹姆斯(1842-1910)、米歇尔·福柯(1926-1984)和海登·怀特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，因此当他们被发现的时候，就是宣告成功的时候。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。+ 第583行：
第573行： − 17世纪左右，伦理学的等级制度在西欧、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。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。站在等级结构中的实体是动物、人类、植物等等。+ 第593行：
第583行： − 以事业为导向的目标可以用层次来描述，描述次要的行动如何支持一个更大的目标。+ 第599行：
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第597行： − 在一些随机的例子中，结构层次之间的“组合”意义是不对称的，因此整个层次数组的小部分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。+ 第615行：
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无编辑摘要
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}}
{{Redirect|Subordinate|other uses|Subordination (disambiguation){{!}}Subordination}}
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 (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).
'''<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”而来）是一组元素（对象、名称、值、类别等）的结构，表示相互之间“之上”“之下”或“同级”关系。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。
一个层次结构可直接或间接地、竖向或对角地将实体联系起来。尽管一个大体上呈层次结构的系统也可以吸收另外的层次结构，一个层次结构中的直接联系——前提是，它们是等级制的——只有与其直接上级或直接下级的联系。层次联系可通过同向的多个联系汇成的路径“垂直”向上或向下发展。层次结构中所有没有垂直相连的部分都可以通过水平路径（向上找到共同直接或间接上级再向下）相连。就像两个同事、同僚各自向共同上级汇报，但他们各自都有同等的相对权限。组织形式的存在对层次结构既是替代也是补充。异质结构也是这样一种形式。
Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below).
Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below).
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"/>
* '''[[Non-physical entity|Object]]''': one entity (e.g., a person, department or [[concept]] or element of arrangement or member of a set)
* '''[[Non-physical entity|Object]]''': one entity (e.g., a person, department or [[concept]] or element of arrangement or member of a set)
*'''<font color="#ff8000">对象 Object</font>'''：一个实体（例如一种成员或配置集的个人、部门、概念、元素）
*'''<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）
* '''[[System]]''': the entire set of objects that are being arranged hierarchically (e.g., an administration)
* '''[[System]]''': the entire set of objects that are being arranged hierarchically (e.g., an administration)
*'''<font color="#ff8000">系统 System</font>'''：层次性配置的整组对象集（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）
* '''[[Dimension]]''': another word for "system" from on-line analytical processing (e.g. cubes)
* '''[[Dimension]]''': another word for "system" from on-line analytical processing (e.g. cubes)
*'''<font color="#ff8000">维度 Dimension</font>'''：联机分析处理（例如立方体）中“系统”的同义词
*'''<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
* '''[[Element (mathematics)|Member]]''': an (element or object) at any (level or rank) in a (class-system, taxonomy or dimension)
* '''[[Element (mathematics)|Member]]''': an (element or object) at any (level or rank) in a (class-system, taxonomy or dimension)
*'''<font color="#ff8000">成员 Member</font>'''：分类系统、分类学或维度中任一层级或位阶一个元素或对象
*'''<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'''
**'''[[Ranking|Rank]]''': the relative [[value (ethics)|value]], worth, [[complexity]], [[Power (philosophy)|power]], importance, [[authority]], level etc. of an object
**'''[[Ranking|Rank]]''': the relative [[value (ethics)|value]], worth, [[complexity]], [[Power (philosophy)|power]], importance, [[authority]], level etc. of an object
**'''<font color="#ff8000">位阶 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
**'''[[wikt:level#Noun|Level]] or Tier''': a set of objects with the same rank OR importance
**'''[[wikt:level#Noun|Level]] or Tier''': a set of objects with the same rank OR importance
**'''<font color="#ff8000">等级 Level</font>'''：同等位阶或重要度的一组对象
**'''<font color="#ff8000">等级 Level</font>'''：阶层或重要度相同的一组对象
**'''[[Order of precedence|Ordering]]''': the arrangement of the (ranks or levels)
**'''[[Order of precedence|Ordering]]''': the arrangement of the (ranks or levels)
**'''<font color="#ff8000">排序 Ordering</font>'''：等级或位阶的配置
**'''<font color="#ff8000">排序 Ordering</font>'''：等级或阶层的配置
**'''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
**'''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
**'''<font color="#ff8000">层次 Hierarchy</font>'''：特定成员组位阶或等级的配置。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'''
**'''[[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: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
**'''<font color="#ff8000">顶 Hierarch</font>'''：层次的顶，位于维度中顶层的一个独立个体（对象或成员）。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
**'''[[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:member|Member]]''', a (member or node) in any level of a hierarchy in a dimension to which (superior and subordinate) members are attached
**'''<font color="#ff8000">构件 Member</font>'''：维系（上级或下级）构件的维度中层次结构里任一层的一个构件或节点
**'''<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
**'''[[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: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
**'''<font color="#ff8000">孤体 Orphan</font>'''：一个没有父级的构件。通常是孤立分支的顶。孤体可通过创建与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。
**'''[[wikt:leaf|Leaf]]''', a member in any level of a dimension without subordinates in the hierarchy
**'''[[wikt:leaf|Leaf]]''', a member in any level of a dimension without subordinates in the hierarchy
**'''<font color="#ff8000">叶 Leaf</font>'''：维度中任一层里没有下级的构件
**'''<font color="#ff8000">叶 Leaf</font>'''：维度中任一层里没有下级的成员
**'''[[wikt:neighbour|Neighbour]]''': a member adjacent to another member in the same (level or rank). Always a peer.
**'''[[wikt:neighbour|Neighbour]]''': a member adjacent to another member in the same (level or rank). Always a peer.
**'''<font color="#ff8000">近邻 Neighbour</font>'''：同一等级或位阶中相邻与另一构件的构件，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。
**'''[[Superior (hierarchy)|Superior]]''': a higher level or an object ranked at a higher level (A parent or an ancestor)
**'''[[Superior (hierarchy)|Superior]]''': a higher level or an object ranked at a higher level (A parent or an ancestor)
** '''[[wikt:peer|Peer]]''': an object with the same rank (and therefore at the same level)
** '''[[wikt:peer|Peer]]''': an object with the same rank (and therefore at the same level)
**'''<font color="#ff8000">同级 Peer</font>'''：同一位阶（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
** '''[[Interpersonal relationship|Interaction]]''': the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair)
** '''[[Interpersonal relationship|Interaction]]''': the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair)
**'''<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。
*'''自然相关的术语 Terms about Nature'''
*'''与自然相关的术语 Terms about Nature'''
** '''[[wikt:attribute|Attribute]]''': a heritable characteristic of (members and their subordinates) in a level (e.g. ''hair-colour'')
** '''[[wikt:attribute|Attribute]]''': a heritable characteristic of (members and their subordinates) in a level (e.g. ''hair-colour'')
大多数层次结构按其主题不同而使用更具体的词汇，但其背后的理念是相同的。例如，在数据结构中，对象称为节点，上级称为父级，下级称为子级。在商业环境中，上级是主管/老板，同级即同事。
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.
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.
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。
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'''<!--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<!--per WP:R#PLA, this SHOULD be bold-->, 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 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.
'''<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。
'''<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。
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.
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.
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）。对许多人来说，“层次”这个词自动唤起了支化层次结构的印象。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。
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.
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.
'''<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。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。
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).
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).
'''<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。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==
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],
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.
“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。
==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==<!--if you change this section's title, please also change the wikilinks throughout the article that link to it! -->
Maslow's hierarchy of human needs. This is an example of a hierarchy visualized with a triangle diagram.]]
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>'''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。
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 (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.
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.
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.
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分明的；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。
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.
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.
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==
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.
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。
# No element is superior to itself, and
# No element is superior to itself, and
# 任何元素都不高于自身，且
# 任何元素都不高于自身，且
# One element, the ''hierarch'', is superior to all of the other elements in the set.
# One element, the ''hierarch'', is superior to all of the other elements in the set.
# 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''层次''元素，高于集合中的所有其他元素。
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 [[Cycle (graph theory)|circular relationships]]; the association between two objects is always [[Transitive relation|transitive]].
{{Main|层次（数学） Hierarchy (mathematics)}}
{{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
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 [[#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.
|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.
数学上，层次结构最一般的形式是'''<font color="#ff8000">偏序集 Partially Ordered Set或Poset</font>'''。元素所组成的系统即整个偏序集。系统内每个元素都共享一些具体无歧义的属性。相同属性的元素可集结成群，最终形成类别层次。
数学上，层次结构最一般的形式是'''<font color="#ff8000">偏序集 Partially Ordered Set或Poset</font>'''。<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>元素所组成的系统即整个偏序集。系统内每个元素都共享一些具体无歧义的属性。相同属性的元素可集结成群，最终形成类别层次。
“层次”专用作指称随复杂度增加而组织的偏序集。例如加法、减法、乘法和除法通常按特定序列实施。一般乘除先于加减，括号也是层次的一种表示，表达了哪些运算优先。例如在(2 + 5) × (7 - 4)中，按数学的层次规则本应先作5乘以7，但加入了括号，则表示了应当先对括号内作运算。在需要多步求解的代数问题上这些规则占主导地位。在数学中使用层次结构有利于快速高效地解决问题，而不必经历漫长的剖析过程。现在认为大多数这类规则是求解特定方程的适当方法。
“层次”专用作指称随复杂度增加而组织的偏序集。例如加法、减法、乘法和除法通常按特定序列实施。一般乘除先于加减，括号也是层次的一种表示，表达了哪些运算优先。例如在(2 + 5) × (7 - 4)中，按数学的层次规则本应先作5乘以7，但加入了括号，则表示了应当先对括号内作运算。在需要多步求解的代数问题上这些规则占主导地位。在数学中使用层次结构有利于快速高效地解决问题，而不必经历漫长的剖析过程。现在认为大多数这类规则是求解特定方程的适当方法。
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 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. 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:
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：
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。
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:
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:
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
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概念始终不变。
'''<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。
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.
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.
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===
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:
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:
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>
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.
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.
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。
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>
<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”。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。
=====组合包容层次结构 Compositional containment hierarchy=====
=====构成性包容层次结构 Compositional containment hierarchy=====
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.<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.
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">组合包容层次结构 Compositional containment hierarchy</font>是组成系统的各个部分的顺序——系统是由这些部分“组成”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。
<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 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.
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.
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。
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.
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.
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分明的。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。社会经济系统被划分为一个社会层级（<font color="#ff8000">社会阶层 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。层级制度如此深入到日常生活中，以至于人们认为它们微不足道。
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"/>
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.
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.
在<font color="#32CD32">反向层次结构 reverse hierarchy</font>中，权力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===
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.
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.
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，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。
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>
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 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.
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.
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===
Many grammatical theories, such as phrase-structure grammar, involve hierarchy.
Many grammatical theories, such as phrase-structure grammar, involve hierarchy.
许多语法理论都包括层次结构，例如短语结构语法。
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.
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===
===Music 音乐===
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 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.
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。在申克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。
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.
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。
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.
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。
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.
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。
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 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.
<font color="#ff8000">伦理学 ethics</font>中列举的各种<font color="#ff8000">美德 virtues</font>，有时根据某些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。
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.
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==
==Examples of other applications 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). -->
<!-- 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的层次结构是什么，它就不属于这里(但这并不意味着如果你能说出它的层次结构是什么，它就属于这里)。-->
<！-- 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)。-->