On strict fuzzy betweenness relations

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

Fuzzy Sets and Systems Pub Date : 2024-11-29 DOI:10.1016/j.fss.2024.109218

Yi Shi

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引用次数: 0

Abstract

Fuzzy betweenness relations have gained increasing attention since Zhang et al. recently established their extensive connections with fuzzy order relations. In this manuscript, we delve into the exploration of strict fuzzy betweenness relations from two aspects. First of all, in light of one of the most important examples of strict betweenness relations from strict order relations, we extend this paradigm to the fuzzy case. Specially, with respect to a t-norm ⁎ and a fuzzy equivalence relation E, we construct a strict ⁎-E-betweenness relation from a strict ⁎-E-order relation. Secondly, by establishing a one-to-one correspondence between strict betweenness relations and betweenness relations, we investigate whether this elegant result persists within the many-valued setting. Toward this end, we present the construction of a strict fuzzy betweenness relation from a fuzzy betweenness relation and vice versa, scrutinizing the conditions under which these constructions are inverse to each other. The conclusion turns out that the correspondence in the fuzzy context exhibits distinct differences from the crisp one, primarily due to the inherent complexity of fuzzy logic.

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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.