Abstract

This paper proposes a new method for solving the problem of multicriteria optimization of a numerical vector function on a fuzzy set. The membership function of a fuzzy feasible set is joined to the original set of criteria that allows the original problem of multi-criteria optimization to be treated as the task of finding a suitable compromise (Pareto-optimal) solution with respect to an extended set of criteria. It is assumed that in a search for the “best” compromise solution there is only fuzzy information about the preferences of decision maker in the form of information quanta. At the first stage of the proposed method, the search for a compromise is made on the basis of an axiomatic approach, with which the Pareto set is reduced. The result of the reduction is a fuzzy set with a membership function, which is determined on the basis of the used fuzzy information. At the second stage, the obtained membership function is added to the extended set of criteria, after which the scalarization procedure based on the idea of goal programming is used to solve the formed multicriteria problem.

中文翻译：

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基于模糊信息的多准则选择

摘要

提出了一种解决模糊集数值向量函数多准则优化问题的新方法。模糊可行集的隶属函数与原始标准集结合在一起，该标准集允许将多准则优化的原始问题视为针对扩展集的适当妥协（帕累托最优）解决方案的任务。标准。假设在搜索“最佳”折衷解决方案时，仅存在关于决策者偏好的模糊信息，其形式为信息量。在所提出的方法的第一阶段，基于公理方法来寻求折衷，通过该方法可以减少帕累托集。减少的结果是具有隶属函数的模糊集，这是根据所使用的模糊信息确定的。在第二阶段，将获得的隶属函数添加到扩展的标准集，然后使用基于目标编程思想的标量过程来解决所形成的多准则问题。