on a Solution Set to a Mathematical Programming Problem with a Fuzzy Set of Constraint Indices

被引：0

作者：

Mashchenko S.O. ^{[1
]}

机构：

[1] Taras Shevchenko National University of Kyiv, Ukraine

来源：

International Journal of Fuzzy System Applications | 2022年 / 11卷 / 01期

关键词：

Decision Maker; Fuzzy Mathematical Programming; Fuzzy Optimization; Fuzzy Set; Fuzzy Set of Operands; Pareto Optimal Alternative; Type-2 Fuzzy Set; Type-2 Membership Function;

D O I：

10.4018/IJFSA.303560

中图分类号：

学科分类号：

摘要：

The present paper investigates a mathematical programming problem with a fuzzy set of constraint indices. To formalize the set of feasible alternatives, the concept of intersection of crisp sets with a fuzzy set of operands is used. The result of this operation is a type-2 fuzzy set (T2FS) (a fuzzy set whose membership function takes a fuzzy set of values). Furthermore, the corresponding membership function is given. It is shown that the T2FS of feasible alternatives can be represented in the form of the collection of T2FSs with constant secondary grades. The notion of the solution T2FS to the mathematical programming problem with a fuzzy set of constraint indices is proposed. The basic properties of the solution T2FS are investigated. The notion of a compromise maximizing solution is given. Several results are proved that make it possible to simplify its construction. Illustrative examples are given. Copyright © 2022, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.

引用

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