Nullnorms on bounded trellises

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-09-19 DOI:10.1016/j.fss.2025.109599

Zhenyu Xiu , Xu Zheng

引用次数: 0

Abstract

In this paper, we first introduce the notion of nullnorms on bounded trellises and investigate their fundamental properties. Then, based on the existence of t-norms, t-conorms, two order-preserving functions, and a conditionally associative, commutative and increasing function, we propose a method for constructing nullnorms on bounded trellises. Finally, we prove that the class of nullnorms on bounded trellises, denoted by

V_{a}

, can be completely characterized by these four components. Meanwhile, our results on nullnorms extend and unify several well-known results in the literature.

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有界格子上的零范数

本文首先引入了有界格子上的零范数的概念，并研究了它们的基本性质。然后，基于t-范数、t-保形、两个保序函数和一个条件结合交换递增函数的存在性，提出了在有界格子上构造零范数的方法。最后，我们证明了用Va表示的有界格子上的零范数可以完全用这四个分量来表征。同时，我们关于零范数的结果扩展和统一了文献中几个著名的结果。

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.