更改

* But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5)

* But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5)

* 它是一个弱帕累托最优，因为没有其他任何分配对上述两个主体是更优的（没有强帕累托改进）。

* 它是一个弱帕累托最优，因为没有其他任何分配对上述两个主体是更优的（没有强帕累托改进）。

* 但它不是一个强帕累托最优，因为这个George在其中得到第二顺位的资源的分配对George是严格更优的且对Alice是弱更优的（它是一个弱帕累托改进），它的分配方案为(10,5)

* 但它不是一个强帕累托最优，因为这个George在其中得到第二顺位的资源的分配对George是严格更优的且对Alice是弱更优的（它是一个弱帕累托改进），它的'''<font color="#32CD32">分配方案</font>'''为(10,5)

As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1).

As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1).

作为一个示例，考虑一个有两个项的项分配问题，Alice 值为3,2，George 值为4,1。考虑将第一个项目分配给 Alice，第二个项目分配给 George，其中'''<font color="#ff8000">分配方案</font>'''为(3,1)。

作为一个示例，考虑一个有两个项的项分配问题，Alice 值为3,2，George 值为4,1。考虑将第一个项目分配给 Alice，第二个项目分配给 George，其中'''<font color="#32CD32">分配方案</font>'''为(3,1)。

* However, it is not fractionally-Pareto-optimal, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George - its utility profile is (3.5, 2).

* However, it is not fractionally-Pareto-optimal, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George - its utility profile is (3.5, 2).

* 它是一个帕累托最优，因为其他任何离散分配（在不分离物品的情况下）都会使得某个主体变差。

* 它是一个帕累托最优，因为其他任何离散分配（在不分离物品的情况下）都会使得某个主体变差。

* 但是，它不是部分帕累托最优的，因为它是受该分配帕累托支配的。它分配给了Alice第一个资源的一半和第二个资源的全部，分配给了George第一个资源的一半。它的分配方案是(3.5,2)。

* 但是，它不是部分帕累托最优的，因为它是受该分配帕累托支配的。它分配给了Alice第一个资源的一半和第二个资源的全部，分配给了George第一个资源的一半。它的'''<font color="#32CD32">分配方案</font>'''是(3.5,2)。

* "The <math>\epsilon</math>-constraints method".<ref>{{cite journal|title=On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization|journal=IEEE Transactions on Systems, Man, and Cybernetics|volume=SMC-1|issue=3|year=1971|pages=296–297|issn=0018-9472|doi=10.1109/TSMC.1971.4308298}}</ref><ref name="Mavrotas2009">{{cite journal|last1=Mavrotas|first1=George|title=Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems|journal=Applied Mathematics and Computation|volume=213|issue=2|year=2009|pages=455–465|issn=00963003|doi=10.1016/j.amc.2009.03.037}}</ref>

* "The <math>\epsilon</math>-constraints method".<ref>{{cite journal|title=On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization|journal=IEEE Transactions on Systems, Man, and Cybernetics|volume=SMC-1|issue=3|year=1971|pages=296–297|issn=0018-9472|doi=10.1109/TSMC.1971.4308298}}</ref><ref name="Mavrotas2009">{{cite journal|last1=Mavrotas|first1=George|title=Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems|journal=Applied Mathematics and Computation|volume=213|issue=2|year=2009|pages=455–465|issn=00963003|doi=10.1016/j.amc.2009.03.037}}</ref>

* “约束法”。

* “ϵ-约束法”。