A note on Chebyshev approximation to an inconsistent system of max-min equations

IF 3.1 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2026-03-15 Epub Date: 2025-11-26 DOI:10.1016/j.fss.2025.109702

Pingke Li

引用次数: 0

Abstract

The consistency of max-min equations is a crucial issue to be concerned when modelling with fuzzy relations in approximate reasoning. An inconsistent system of max-min equations may be perturbed slightly to restore the consistency. This paper tackles the inconsistency resolving problem by means of Chebyshev approximation, i.e., minimizing the maximum absolute deviation in both the coefficient matrix and right-hand side vector. It demonstrates that the minimum deviation level for consistency may be obtained by a polynomial-time direct search method. A Chebyshev approximation is constructed accordingly with the number of modified elements in the coefficient matrix as few as possible.

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不一致极大极小方程组的切比雪夫近似

在近似推理中用模糊关系建模时，极大极小方程的一致性是一个非常重要的问题。一个不一致的极大极小方程系统可以稍加扰动以恢复其一致性。本文用切比雪夫近似解决了不一致问题，即系数矩阵和右侧向量的最大绝对偏差都最小化。结果表明，用多项式时间直接搜索法可以求出一致性的最小偏差水平。在系数矩阵中修改元素的数目尽可能少的情况下，构造了切比雪夫近似。

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.