Geometric properties of ternary fuzzy relations

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

Fuzzy Sets and Systems Pub Date : 2024-11-08 DOI:10.1016/j.fss.2024.109188

Bin Pang , Xiu-Yun Wu , Bernard De Baets

引用次数: 0

Abstract

Ternary fuzzy relations, and fuzzy betweenness relations in particular, are witnessing increasing attention in recent years. A key reason is that axiomatic properties of ternary fuzzy relations seem to be ideally suited to capture geometric characteristics of the abstract notion of betweenness. In this paper, we introduce several new properties of ternary fuzzy relations, including the Peano property, the Pasch property and the sand-glass property, that can be qualified as geometric properties. We investigate their interrelationships as well as their connections with various types of fuzzy betweenness relations. Additionally, in the context of our study of the Pasch property and the sand-glass property, we introduce the convexity property of ternary fuzzy relations by taking inspiration from the solid theoretical basis of the theory of fuzzy convex structures.

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三元模糊关系的几何特性

近年来，三元模糊关系，尤其是模糊间性关系越来越受到关注。其中一个重要原因是，三元模糊关系的公理性质似乎非常适合捕捉抽象的 "间性 "概念的几何特征。在本文中，我们介绍了三元模糊关系的几个新性质，包括 Peano 性质、Pasch 性质和沙漏性质，它们都可以被定性为几何性质。我们研究了它们之间的相互关系，以及它们与各种模糊间性关系的联系。此外，在研究帕施性质和沙漏性质的过程中，我们从模糊凸结构理论的坚实理论基础中得到启发，引入了三元模糊关系的凸性质。

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.