Ordinal sums of triangular norms on a bounded trellis

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

Fuzzy Sets and Systems Pub Date : 2025-05-08 DOI:10.1016/j.fss.2025.109440

Jun Geng , Ziwen Chen , Rina Wang

引用次数: 0

Abstract

In this paper, we present ordinal sums of triangular norms on bounded trellises with one summand firstly by taking a right-transitive element as the left endpoint and a ∧-associative element as the right endpoint of the given interval sub-trellis. Also, the corresponding recursive construction of triangular norms on bounded trellises is shown. Meanwhile, we extend the result to the ordinal sums of triangular norms on bounded trellises with more summands including two cases that the given interval sub-trellises are contiguous or not. Particularly, we can naturally obtain two classes of triangular norms which are different from others on bounded lattices. And some illustrative examples are added for clarity.

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有界格子上三角模的序数和

本文首先以一个右传递元作为给定区间子格的左端点，一个∧结合元作为给定区间子格的右端点，给出了带一个和的有界格上三角模的序数和。同时，给出了有界格子上三角形范数的递推构造。同时，我们将结果推广到具有更多和的有界格子上的三角模的序数和，包括给定区间子格子相邻或不相邻的两种情况。特别地，我们可以很自然地得到两类不同于其他有界格上的三角模。为了清晰起见，还添加了一些说明性的例子。

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.