Subsethood measures based on cardinality of type-2 fuzzy sets

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

Fuzzy Sets and Systems Pub Date : 2024-11-04 DOI:10.1016/j.fss.2024.109174

Carmen Torres-Blanc , Jesus Martinez-Mateo , Susana Cubillo , Luis Magdalena , Francisco Javier Talavera , Jorge Elorza

引用次数: 0

Abstract

In this work we present a novel axiomatic framework for subsethood measures in type-2 fuzzy sets. It differs from previous approaches in two key ways. First, the degree of membership is not simply a fuzzy set as considered in other papers, but rather a label of the variable Truth, more in line with Zadeh's original idea. Secondly, the concept of subsethood is approached in terms of its relationship with cardinality. Additionally, illustrative examples of such measures are provided.

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基于第 2 类模糊集心率的次优度量

在这项研究中，我们提出了一个新颖的公理框架，用于研究 2 型模糊集合中的子实体度量。它在两个关键方面不同于以往的方法。首先，成员度并不像其他论文所考虑的那样只是一个模糊集，而是变量 Truth 的一个标签，这更符合 Zadeh 最初的想法。其次，子实体的概念是根据其与万有引力的关系来处理的。此外，还提供了此类度量的示例。

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.