Composition as a fuzzy conjunction between indexes of inclusion

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

Fuzzy Sets and Systems Pub Date : 2026-03-15 Epub Date: 2025-11-21 DOI:10.1016/j.fss.2025.109685

Nicolás Madrid, Manuel Ojeda-Aciego

引用次数: 0

Abstract

We analyze the use of the composition of mappings as a fuzzy conjunction between indexes of inclusion. Instead of the general approach of the φ-index of inclusion, we consider a fresh approach that computes the φ-index of inclusion when restricted to a join-subsemilattice of indexes of inclusion. Under this restriction, we identify a certain join-subsemilattice which has a biresiduated structure when composition is interpreted as conjunction. The main consequence of this biresiduated structure is a representation theorem of biresiduated lattices on the unit interval in terms of the composition and subsets of indexes of inclusion.

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作为包含指标之间的模糊连接的组合

我们分析了使用映射的组合作为包含指标之间的模糊连接。我们考虑了一种新的方法来代替一般的包含指数的φ指数计算方法，这种方法是在包含指数的连接-子半格中计算包含指数的φ指数。在此限制下，我们确定了当组合解释为合时具有双残结构的某一连接-亚半格。这个双残结构的主要结论是单位区间上关于包含指标的组合和子集的双残格的表示定理。

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.