一类二位函数的一些代数和分析性质

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

Fuzzy Sets and Systems Pub Date : 2024-11-15 DOI:10.1016/j.fss.2024.109196

Xue-ping Wang, Yun-Mao Zhang

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引用次数: 0

摘要

本文讨论由一元函数 f:[0,1]→[0,1] 和二元函数 F:[0,1]2→[0,1] 生成的公式 f(-1)(F(f(x),f(y)))。当 f 是严格递增函数，F 是连续、非递减、关联函数且中性元素在 [0,1] 时，研究公式的以下代数和分析性质：幂等元素、连续性（左连续性/右连续性）、关联性和极限性质。研究了这些性质之间的关系。给出了公式成为三角形规范（即三角形 conorm）的一些必要条件和一些充分条件。特别是，给出了获得连续阿基米德三角形规范（或三角形 conorm）的必要条件和充分条件。当 f 是非递减的注入函数且 F 是非递减的关联函数且中性元素在 [0,1] 时，我们研究了公式的关联性。

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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Some algebraic and analytical properties of a class of two-place functions

This article deals with the formula

f^{(- 1)} (F (f (x), f (y)))

generated by a one-place function

f : [0, 1] \to [0, 1]

and a binary function

F : {[0, 1]}^{2} \to [0, 1]

. When the f is a strictly increasing function and F is a continuous, non-decreasing and associative function with neutral element in

[0, 1]

, the following algebraic and analytical properties of the formula are studied: idempotent elements, the continuity (resp. left-continuity/right-continuity), the associativity and the limit property. Relationship among these properties is investigated. Some necessary conditions and some sufficient conditions are given for the formula being a triangular norm (resp. triangular conorm). In particular, a necessary and sufficient condition are expressed for obtaining a continuous Archimedean triangular norm (resp. triangular conorm). When the f is a non-decreasing surjective function and F is a non-decreasing associative function with neutral element in

[0, 1]

, we investigate the associativity of the formula.

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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.