P-sets

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

Fuzzy Sets and Systems Pub Date : 2024-12-17 DOI:10.1016/j.fss.2024.109244

Eszter K. Horváth , Leonard Kwuida , Branimir Šešelja , Andreja Tepavčević

引用次数: 0

Abstract

Starting from a poset P and a set A, we introduce P-sets as a natural generalization of Ω-sets. A P-set on A is defined by adding to A a special map from

A^{2}

to P, which generalizes the classical equality relation. We prove that P-sets on A are naturally obtained from centralized closure systems in a family of all weak equivalences on A. Moreover, for every P-set there is a canonical representation in which the used centralized closure system replaces the poset P.

Further, we present a classification of all P-sets by the family of cuts, where A and P are fixed. Different P-sets may have equal collections of cut sets. Necessary and sufficient conditions under which this happens are presented; i.e., all P-sets are classified according to the equality of collections of cut sets.

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从正集 P 和集合 A 开始，我们引入 P 集作为 Ω 集的自然概括。A 上的 P 集是通过在 A 上添加一个从 A2 到 P 的特殊映射来定义的，它是对经典相等关系的概括。我们证明，A 上的 P 集是由 A 上所有弱等价关系族中的集中闭合系统自然获得的。此外，对于每个 P 集，都有一个规范表示，其中使用的集中闭合系统取代了 P 正集。不同的 P 集可能有相同的切集集合。我们提出了发生这种情况的必要条件和充分条件；也就是说，所有 P 集都是根据切集集合的相等性来分类的。

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.