In Crisp environment, the notion of cyclic group on a set is well known. We study an extension of this classical notion to the Mfuzzy sets to define the concept of Mcyclic fuzzy groups. By using these cyclic ,M-fuzzy groups, we then define cyclic M-fuzzy group family and investigate its structure properties with applications. 2000AMS Subject classification: 08A72 , 20N25, 03E72, 94D05

In this article, a measure that quantifies the relational structure within and between groups is proposed, comprising not only analysis of disjoint or non-disjoint groups, but also fuzzy groups. This based on existing known as EI index. The current index homophily applied to networks with presence although large scale rarely exist in many empirical networks. addition, combination edge node weig...

Fuzzy groups and fuzzy theory have a lot of applications in several sciences such as mathematics, computer science, computer and electrical engineering. Hence, counting the number of fuzzy subgroups of finite groups to classify them is an important issue in fuzzy theory. The Main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group 1 2 3 k...

In this paper we introduce the smallest equivalence relation ξ∗ on a finite fuzzy hypergroup S such that the quotient group S/ξ∗, the set of all equivalence classes, is a solvable group. The characterization of solvable groups via strongly regular relation is investigated and several results on the topic are presented.

One of the most important problems of fuzzy group theory is to classify the fuzzy subgroups of a finite group. This topic has enjoyed a rapid development in the last few years. Several papers have treated the particular case of finite abelian groups. Thus, in [13] the number of distinct fuzzy subgroups of a finite cyclic group of square-free order is determined, while [14–16] and [28] deal with...

The purpose of this note is to give an example to counter the result of [5] and to find the cardinality of the image of a fuzzy symmetric subgroups of S4, S5 and Sn. Mathematics Subject Classification: 03G10, 20B30, 20B35

In this paper a first step in classifying the fuzzy normal subgroups of a finite group is made. Explicit formulas for the number of distinct fuzzy normal subgroups are obtained in the particular cases of symmetric groups and dihedral groups.