Inverses of fuzzy relation matrices with addition-min composition

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-06-07 DOI:10.1016/j.fss.2024.109037

Fang-Fang Guo , Rong Fu , Jie Shen

引用次数: 0

Abstract

This paper mainly considers the post-inverse matrix of a fuzzy relation matrix in terms of addition-min composition. A necessary and sufficient condition for the consistency of the inverse matrix problem is given by transforming the problem into a series of particular fuzzy relation equations. The uniqueness of the post-inverse is also investigated. Furthermore, it is proved that the search for the minimal solutions of the particular fuzzy relation equations can be converted into solving a linear system. Based on these discussions, an algorithm is constructed for solving a post-inverse of a given fuzzy relation matrix.

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模糊关系矩阵的加分-减分构成的倒数

本文主要从加减法构成的角度考虑模糊关系矩阵的后逆矩阵。通过将问题转化为一系列特定的模糊关系方程，给出了逆矩阵问题一致性的必要条件和充分条件。还研究了后逆的唯一性。此外，还证明了寻找特定模糊关系方程的最小解可以转换为求解线性系统。在这些讨论的基础上，构建了一种求解给定模糊关系矩阵后逆的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.