New results on α-cuts of type-2 fuzzy sets

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Fuzzy Sets and Systems Pub Date : 2024-10-17 DOI:10.1016/j.fss.2024.109152

Wei Zhang , Bao Qing Hu

引用次数: 0

Abstract

The α-cut (i.e., α-plane) of type-2 fuzzy sets is a very useful tool for computation. However, there are some theoretical mistakes in type-2 fuzzy sets literature discussing the topic of α-cuts. This paper will illustrate these mistakes through examples and specifically address the two new questions induced by them: (1) Taking the α-cut (resp. α-strong cut) of the result obtained by performing a T-extension operation of ⁎ (i.e., t-norm extension operation of a general binary operation) on two type-2 fuzzy sets is equal to what? (2) What conditions are required for taking the α-cut (resp. α-strong cut) of the result obtained by performing a T-extension operation of ⁎ on two type-2 fuzzy sets to be equal to performing the ⁎ operation on the α-cuts (resp. α-strong cuts) of these two type-2 fuzzy sets? Finally, we will get a comprehensive answer to these two questions.

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关于 2 型模糊集 α 切分的新成果

2 型模糊集的 α 切（即 α 平面）是一种非常有用的计算工具。然而，在讨论 α 切的主题时，2 型模糊集文献中存在一些理论错误。本文将通过实例来说明这些错误，并具体讨论由这些错误引发的两个新问题：（1）取对⁎进行 T-扩展操作（即、(2) 在两个 2 型模糊集合上执行⁎的 T 扩展操作（即一般二进制操作的 t-norm 扩展操作）得到的结果的 α 切（即 α-强切）等于在这两个 2 型模糊集合的 α 切（即 α-强切）上执行⁎操作，需要什么条件？最后，我们将得到这两个问题的综合答案。

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.

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