Generating quasi-t-subnorms on preordered sets via Adjunctions and Left Galois Connections

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

Fuzzy Sets and Systems Pub Date : 2024-06-07 DOI:10.1016/j.fss.2024.109036

Jun Geng , Rina Wang , Ziwen Chen

引用次数: 0

Abstract

In this paper, we investigate several classes of binary operations within the preordered framework. First, we give the definition of quasi-t-subnorm on preordered sets. Subsequently, we research two classes of quasi-t-subnorms by means of Adjunctions and Left Galois Connections respectively. Meanwhile, we introduce new preorders differing from the inclusion order on powersets. Importantly, quasi-t-subnorms can be defined on powersets with preorders. Then we get a class of extensive binary operations via Adjunctions between preordered sets and the preordered sets consisting of powersets, which generalizes the previous results. The relationship between related binary operations is explored at last.

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通过邻接和左伽罗瓦连接生成预序集上的准 T 次规范

本文研究了预排序框架内的几类二元运算。首先，我们给出了预序集上的准 t 次规范的定义。随后，我们分别通过邻接和左伽罗瓦连接研究了两类准 t 次矩阵。同时，我们引入了不同于幂集包含阶的新预序。重要的是，准 t 次矩阵可以定义在有前序的权集上。然后，我们通过前序集和由幂集组成的前序集之间的 Adjunctions 得到了一类广泛的二进制运算，从而推广了之前的结果。最后，我们探讨了相关二进制运算之间的关系。

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.