Terms that define nuclei on residuated lattices: A case study of BL-algebras

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

Fuzzy Sets and Systems Pub Date : 2025-07-25 DOI:10.1016/j.fss.2025.109542

Sebastián Buss , Diego Castaño , José Patricio Díaz Varela

引用次数: 0

Abstract

A nucleus γ on a (bounded commutative integral) residuated lattice A is a closure operator that satisfies the inequality

γ (a) \cdot γ (b) \leq γ (a \cdot b)

for all

a, b \in A

. In this article, among several results, a description of an arbitrary nucleus on a residuated lattice is given. Special attention is given to terms that define a nucleus on every structure of a variety, as a means of generalizing the double negation operation. Some general results about these terms are presented, together with examples. The main result of this article consists of the description of all terms of this kind for every given subvariety of BL-algebras. We exhibit interesting nontrivial examples.

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在剩余格上定义核的术语：bl -代数的一个案例研究

（有界交换积分）残差格A上的核γ是一个闭包算子，它满足不等式γ(A)⋅γ(b)≤γ(A·b)，对于所有A，b∈A。在一些结果中，给出了任意核在剩余晶格上的描述。特别注意在一个品种的每一个结构上定义一个核的术语，作为推广双重否定操作的一种手段。给出了关于这些术语的一些一般结果，并举例说明。本文的主要结果包括对每一个给定的bl -代数子簇的所有这类项的描述。我们将展示一些有趣的非平凡的例子。

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.