A note on the cross-migrativity between uninorms and overlap (grouping) functions

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Fuzzy Sets and Systems Pub Date : 2024-11-15 DOI:10.1016/j.fss.2024.109190

Xiangjie Fang, Kuanyun Zhu

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引用次数: 0

Abstract

In 2022, Zhu et al. [14] studied the α-cross-migrativity between uninorms and overlap (grouping) functions, and mainly characterized in detail the corresponding cross-migrativity property when uninorms belong to five general classes (i.e.,

U_{\min}

U_{\max}

U_{i d e}

U_{r e p}

and

U_{\cos}

), respectively. However, the results obtained by Zhu et al. have some defects, such as lengthy (or unclear) proofs, false proofs and faulty conclusions. Therefore, this paper indicates the defects and reasons, and the corresponding correction. In addition, some further conclusions are given, which relates the α-cross-migrativity between uninorms and overlap (grouping) functions to α-cross-migrativity between t-norms (t-conorms) and overlap (grouping) functions.

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关于非矩阵和重叠（分组）函数之间交叉迁移性的说明

2022年，Zhu等人[14]研究了非矩形与重叠（分组）函数之间的α交叉迁移性，主要详细表征了非矩形分别属于5个一般类（即Umin、Umax、Uide、Urep和Ucos）时相应的交叉迁移性质。然而，Zhu 等人得到的结果存在一些缺陷，如证明冗长（或不清晰）、虚假证明和错误结论等。因此，本文指出了这些缺陷及其原因，并进行了相应的修正。此外，本文还给出了一些进一步的结论，将非矩形与重叠（分组）函数之间的α-交叉迁移性与 t-矩形（t-conorms）与重叠（分组）函数之间的α-交叉迁移性联系起来。

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.