Many-valued aspects of tense and related operators

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-06-16 DOI:10.1016/j.fss.2025.109509

Michal Botur , Jan Paseka , Richard Smolka

引用次数: 0

Abstract

Our research builds upon Halmos's foundational work on functional monadic Boolean algebras and our previous work on tense operators to develop three essential constructions, including the important concepts of fuzzy sets and powerset operators. These constructions have widespread applications across contemporary mathematical disciplines, including algebra, logic, and topology. The framework we present generates four covariant and two contravariant functors, establishing three adjoint situations.

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时态和相关操作符的多值方面

我们的研究建立在Halmos关于泛函一元布尔代数的基础工作和我们之前关于紧算子的工作的基础上，发展了三个基本结构，包括模糊集和幂集算子的重要概念。这些结构在当代数学学科中有广泛的应用，包括代数、逻辑和拓扑学。我们提出的框架产生了四个协变函子和两个逆变函子，建立了三种伴随情况。

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.