Fuzzy Green's relations and its applications in E-fuzzy semigroups

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

Fuzzy Sets and Systems Pub Date : 2025-06-03 DOI:10.1016/j.fss.2025.109482

Yuan Zhi , Qingguo Li , Xiangnan Zhou

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引用次数: 0

Abstract

Within the framework of fuzzy algebras with fuzzy equality and a complete lattice for membership values, this paper introduces a novel fuzzified version of classical Green's relations on E-fuzzy semigroups, referred to as E-fuzzy Green's relations. We reveal several properties of E-fuzzy semigroups, including the properties of fuzzy unit elements within E-fuzzy cancellative semigroups. Additionally, we derive equivalent forms of these newly defined fuzzy relations and examine the properties of their associated cut-quotient structures in certain E-fuzzy semigroups. The E-fuzzy Green's relations on E-fuzzy semigroups are found to be compatible fuzzy equivalence relations (fuzzy equalities) on some E-fuzzy bands. Furthermore, we present two significant decomposition theorems related to the cut-quotient structures over fuzzy Green's relations, demonstrating that these structures have additional algebraic properties compared with the quotient structures over ordinary fuzzy equality

E^{μ}

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模糊格林关系及其在e -模糊半群中的应用

在具有模糊等式和隶属值完备格的模糊代数框架内，引入了e -模糊半群上经典格林关系的一种新的模糊化形式，称为e -模糊格林关系。给出了e -模糊半群的若干性质，包括e -模糊可消半群内模糊单位元的性质。此外，我们导出了这些新定义的模糊关系的等价形式，并研究了它们在某些e -模糊半群中所关联的切商结构的性质。在某些E-fuzzy带上，发现E-fuzzy半群上的E-fuzzy格林关系是相容的模糊等价关系（模糊等式）。此外，我们给出了模糊格林关系上的切商结构的两个重要分解定理，证明了这些结构与普通模糊等式上的商结构相比具有额外的代数性质。

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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.