The various fuzzy subgroups of a group which are admissible under operator domains are studied. In particular, the classes of all inner automorphisms, automorphisms, and endomorphisms are applied on the fuzzy subgroups of a group. As results, several theorems and examples concerning the fuzzy subgroups following from these kinds of operator domains are obtained. Moreover, we prove that a necess...

in this paper we study a representation of a fuzzy subgroup $mu$ of a group $g$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  this representation is unique up to the number of components and their isomorphic copies. in the crisp group theory, this is a well-known theorem attributed to remak, krull, and schmidt. we consider the lattice of fuzzy subgroups and som...

In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and som...

in this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

in this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.we also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

In this article we will use the redefined definition of a fuzzy subgroup as in [1], and will mainly prove that if G, G are two groups and f: G G' is an epirnorphism, then there is a bijection between the set of all fuzzy subgroups of G/Ker f and that of G .

in this paper, we examine that some simple $k_4$-groups can be determined uniquely by their orders and one or two irreducible complex character degrees.

In this paper, we introduce the concept of an anti M-fuzzy subgroup of an M-group and lower level subset of an anti M-fuzzy subgroup and discussed some of its properties.

The complex fuzzy environment is an innovative tool to handle ambiguous situations in different mathematical problems. In this article, we commence the abstraction of (?,?)-complex sets, subgroupoid, subgroups and describe important examples symmetric group under sets. Additionally, discuss conjugacy class with respect normal subgroups. We define cosets elaborate upon certain operation analog t...