表征 T 子群在聚合情况下保持不变的新型支配力

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

Fuzzy Sets and Systems Pub Date : 2024-09-30 DOI:10.1016/j.fss.2024.109139

Francisco Javier Talavera , Sergio Ardanza-Trevijano , Jean Bragard , Jorge Elorza

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引用次数: 0

摘要

本研究以有关聚合算子保留模糊结构的结果为基础。我们分析了聚合算子在什么情况下会保留 T 子群的结构，这是此类算子表征中尚未解决的最后一种情况。为了描述不同群组的这些算子，我们引入了松弛的支配形式，并研究了它们的性质和相互联系。我们还全面回顾了聚合算子在保留任意群的 T 子群时必须满足的特征。

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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New types of domination to characterize the preservation of T-subgroups under aggregation

This study builds upon results concerning the preservation of fuzzy structures by aggregation operators. We analyze when an aggregation operator preserves the structure of T-subgroup in the last cases remaining unresolved in the characterization of such operators. In order to characterize these operators for different groups, relaxed forms of domination are introduced and their properties and interconnections are studied. We also include a thorough review of the features that an aggregation operator must fulfill to preserve T-subgroups of an arbitrary group.

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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.