Idempotent measures: Monads, convexities and a fuzzy integral

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

Fuzzy Sets and Systems Pub Date : 2024-08-08 DOI:10.1016/j.fss.2024.109100

Taras Radul

引用次数: 0

Abstract

We explore the isomorphism between the idempotent measure monad, which relies on the maximum and addition operations, and the idempotent measure monad, which is built upon the maximum and multiplication operations. One of the implications of this result is the development of a fuzzy integral that utilizes the maximum and addition operations. Additionally, we delve into the study of convexities associated with these monads.

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幂等度量：单子、凸性和模糊积分

我们探讨了依赖于最大值和加法运算的幂等度量一元体与建立在最大值和乘法运算基础上的幂等度量一元体之间的同构性。这一结果的意义之一是开发了一种利用最大值和加法运算的模糊积分。此外，我们还深入研究了与这些单子相关的凸性。

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.