The multiplicative Cauchy equation on [0,1] and its application to the quasi-homogeneity equation

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

Fuzzy Sets and Systems Pub Date : 2024-06-25 DOI:10.1016/j.fss.2024.109052

Yong Su , Wenwen Zong , Radko Mesiar , Radomír Halaš

引用次数: 0

Abstract

The (extended) homogeneity plays important, and often crucial role in economics, decision making and image processing. When studying the quasi-homogeneity equation, the multiplicative Cauchy equation on $[0, 1]$ naturally appears. However, after a detailed analysis of its existing solutions it turned out that some solution of (extended) homogeneity equation was missing. The aim of the paper is to present a complete list of solutions of the multiplicative Cauchy equation and then to give the missing solution of quasi-homogeneity equation from the previous work. For a triangular norm T, we introduce a new concept of T-quasi-homogeneity and, for a strict t-norm T, we clarify the link between the quasi-homogeneity and the T-quasi-homogeneity.

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[0,1]上的考奇乘法方程及其在准均质性方程中的应用

扩展）同质性在经济学、决策制定和图像处理中发挥着重要的作用，而且往往是关键性的作用。在研究准均质性方程时，自然会出现 [0,1] 上的乘法考奇方程。然而，在对其现有解法进行详细分析后发现，（扩展的）同质性方程缺少某种解法。本文的目的是列出乘法考希方程的完整解，然后给出前人工作中缺失的准均质方程的解。对于三角形规范 T，我们引入了 T-准均质性这一新概念；对于严格 t 规范 T，我们阐明了准均质性与 T-准均质性之间的联系。

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.