A note on t-norms having additive generators

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

Fuzzy Sets and Systems Pub Date : 2024-10-31 DOI:10.1016/j.fss.2024.109172

Wenwen Zong , Yong Su , Radko Mesiar

引用次数: 0

Abstract

This paper focuses on t-norms which have some additive generators. We show that a t-norm T has some additive generators if and only if the fully ordered semigroup induced by T can be embedded into some fully ordered semigroup induced by either the product

T_{P}

or the Lukasiewicz t-norm

T_{L}

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关于具有相加生成器的 t 准则的说明

本文重点研究具有一些可加生成器的 t-norms 。我们证明，当且仅当 T 所诱导的完全有序半群可以嵌入到乘积 TP 或卢卡西维茨 t-norm TL 所诱导的完全有序半群中时，t-norm T 才有一些可加生成器。

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.