Domination Structures and Nondominated Solutions
Domination Structures and Nondominated Solutions
复制标题
支配结构和非支配解
DOI：
10.1007/978-1-4684-8395-6_7
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发表时间：
1975
影响因子：
4.2
通讯作者：
P. Yu
中科院分区：
文献类型：
--
作者：
P. Yu
在第三章中，我们讨论了“帕累托偏好”是基于“越多越好”的假设，没有其他偏好信息的假设。这是最简单的一种偏好。回想一下，帕累托偏好不是弱序，因为诱导无差异关系{~}不是传递的。另一方面，从第4-6章我们知道，与折衷解相关联的值函数或距离函数必须假设相应的偏好{}是弱序，并且诱导无差异曲线必须包含关于{}的可数稠密子集。假设{\displaystyle {\frac {frac}的值函数表示肯定是非常严格的，正如第5章所讨论的。帕累托偏好假设与偏好具有价值函数表示的假设之间的差距非常大。
In Chapter 3 we discussed that “Pareto preference” is based on the assumption that “more is better,” with no other preference information assumed. This is the simplest kind of preference. Recall that Pareto preference is not a weak order because the induced indifference relation, {~}, is not transitive. On the other hand, from Chapters 4–6, we know that a value function or distance function associated with a compromise solution must assume that the corresponding preference {≻} is a weak order and the induced indifference curves must contain a countable dense subset with respect to {≻}. The assumptions for {≻} to have a value function representation certainly are very restrictive, as discussed in Chapter 5. The gap between the assumption of Pareto preference and that of the preference having a value function representation is very large.