无零除数三角规范算子实现的直接积和序积

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

Fuzzy Sets and Systems Pub Date : 2024-07-29 DOI:10.1016/j.fss.2024.109096

Joseph McDonald

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引用次数: 0

摘要

在本论文中，我们将继续 Chon 以及 Mezzomo、Bedregal 和 Santiago 的工作，研究模糊正集和有界模糊网格的代数运算。我们首先证明，只要实现乘积构造的三角规范没有零除数，模糊正集在有限直接乘积下就是封闭的。然后将这一结果扩展到有界模糊网格的情况。然后，在没有零穷元素的三角规范以及严格单调和可取消三角规范实现的直接积的情况下，我们得到了一些直接结果。然后，我们引入了基于三角形规范的序积构造，并同样证明了只要实现积构造的三角形规范没有零除数，模糊正集在序积下就是封闭的。

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Direct and ordinal products realized by triangular norm operators with no zero divisors

In this note we continue the work of Chon, as well as Mezzomo, Bedregal, and Santiago, by studying algebraic operations on fuzzy posets and bounded fuzzy lattices. We first prove that fuzzy posets are closed under finite direct products whenever the triangular norm realizing the product construction has no zero divisors. This result is then extended to the case of bounded fuzzy lattices. Some immediate consequences are then obtained within the setting of direct products realized by triangular norms with no nilpotent elements as well as strictly monotone and cancellative triangular norms. We then introduce a triangular norm based construction of ordinal products and similarly show that fuzzy posets are closed under ordinal products whenever the triangular norm realizing the product construction has no zero divisors.

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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.