The notion of an n-ary group is a natural generalization of the notion of a group and has many applications in different branches. In this paper, the notion of (normal) fuzzy n-ary subgroup of an n-ary group is introduced and some related properties are investigated. Characterizations of fuzzy n-ary subgroups are given.

Using s-norm S, we introduce the notion of sensible fuzzy R-subgroups in near-rings, and some related properties are investigated. Mathematics Subject Classification: 06F35, 03G25, 03E72.

In this paper, we treat accounting for the number of fuzzy (normal) subgroups finite groups U6n. order to do this, use natural equivalence relation on set U6n, which has a consistent group theoretical foundation. fact, corresponding classes U6n are closely connected structure lattice and chains terminate in regards, Inclusion-Exclusion principle plays an essential role some situations leads rec...

Bentea and Tu{a}rnu{a}uceanu~(An. c{S}tiinc{t}. Univ. Al. I.Cuza Iac{s}, Ser. Nouv{a}, Mat., {bf 54(1)} (2008), 209-220)proposed the following problem: Find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$Q_8times mathbb{Z}_n$ where $Q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. In this paper weconsider more general grou...

As an abstraction of the geometrical notion of translation, the first author has already introduced two operators T+ and T-called the intuitionistic fuzzy translation operators on the intuitionistic fuzzy sets and studied their properties and investigate theaction of these operators on intuitionistic fuzzy subgroups of a group in [11]. The concept of intuitionistic M-fuzzy subgrou...

Fuzzy clustering is a data analysis technique that, when applied to a set of heterogeneous items, identifies homogenous subgroups as defined by a given model or measure of similarity in fuzzy environment. Moreover, fuzzy clustering methodology has been developed and used in variety of areas like biology, computer science, engineering, medicine etc. In this paper, fuzzy cluster model is develope...