Abstract

A problem of multicriteria optimization on a fuzzy set specified by its membership function is considered. A two-step approach is proposed to solve this problem. It involves searching for a compromise between the available criteria and the membership function. At the first stage, a new vector criterion is formed by adding the membership function to the set of initial criteria and information about the importance of criteria in the form of quanta of information is used to reduce the Pareto set. If the reduced Pareto set is not chosen as the final solution to the multicriteria optimization problem, scalarization that uses the concept of ​​goal programming is proposed at the second stage.

中文翻译：

---

模糊集的多准则选择作为折衷搜索问题

摘要

考虑了由隶属函数指定的模糊集的多准则优化问题。提出了一种两步法来解决这个问题。它涉及在可用标准和隶属函数之间寻找折衷方案。在第一阶段，通过将隶属函数添加到初始标准集合中来形成新的向量标准，并且以信息量形式使用关于标准重要性的信息来减少帕累托集合。如果未选择简化的Pareto集作为多准则优化问题的最终解决方案，则在第二阶段提出使用目标规划概念的标量化。