有理均值，均值的弱结合性，均值类型和t-（范数，规范）映射及其应用的不变性

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

Fuzzy Sets and Systems Pub Date : 2025-02-25 DOI:10.1016/j.fss.2025.109334

Anna Gołecka , Tomasz Małolepszy , Janusz Matkowski

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引用次数: 0

摘要

考虑了均值和t规范。引入了连接这两个函数族的加权拟算术均值的弱结合性。我们观察到，每一个t范数的对称性都来自于对其余公理的一个修正系统。给出了有理函数在（0,∞）上是二元齐次均值的条件。研究了均值型映射和t-（范数，保角）型映射的均值和函数的不变性。

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Rational means, weak associativity of means, invariance with respect to mean-type and t-(norm,conorm) mappings and applications

The means and t-norms are considered. A weak associativity property of the weighted quasi-arithmetic means, connecting these two families of functions, is introduced. It is observed that the symmetry of every t-norm follows from a modified system of the remaining axioms. The conditions under which a rational function is a bivariate homogeneous mean in

(0, \infty)

are given. The invariance of means and functions with respect to the mean-type mappings and t-(norm,conorm)-type mappings is considered with some applications.

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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.