Maximum-interval solutions of the given solution for system of addition-min fuzzy relational inequalities

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

Fuzzy Sets and Systems Pub Date : 2025-03-17 DOI:10.1016/j.fss.2025.109369

Yan-Kuen Wu , Ching-Feng Wen , Yuan-Teng Hsu

引用次数: 0

Abstract

For a given solution to the addition-min fuzzy relational inequalities (FRIs) system, the maximum amplitude (the largest possible deviation from the given solution) and maximum-amplitude solution are proposed to measure its stability. In this paper, we formulate a single-variable optimization model and present some properties to the maximum amplitude. Based on these properties, an algorithm is proposed, which can quickly obtain the maximum amplitude and maximum-amplitude solution of the problem without decomposing the system into multiple subproblems. Additionally, the minimal solution associated with the maximum-amplitude solution can be derived by using the existing algorithm. By examining the relationship between the obtained minimal solution and the given solution, we are able to derive the maximum-interval solution. This maximum-interval solution is generally more “stable” than the maximum-amplitude solution for the addition-min FRIs system.

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加法最小模糊关系不等式系统给定解的最大区间解

对于加最小模糊关系不等式（FRIs）系统的给定解，提出了最大幅值（与给定解的最大可能偏差）和最大幅值解来衡量其稳定性。在本文中，我们建立了一个单变量优化模型，并给出了最大振幅的一些性质。在此基础上，提出了一种算法，该算法无需将系统分解为多个子问题，即可快速获得问题的最大幅值和最大幅值解。此外，利用已有的算法还可以推导出与最大振幅解相关联的最小解。通过检验得到的最小解与给定解之间的关系，我们可以推导出最大区间解。对于最小相加fri系统，这种最大区间解通常比最大振幅解更“稳定”。

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.