Using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyHv-ideal of an Hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. Since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy Hv-ideals is an important and ...

The main objective of subgroup discovery is to discover interesting and interpretable patterns with respect to a specific property. The use of evolutionary fuzzy systems provides good algorithms to approach this problem. In this sense, NMEEF-SD algorithm –one of the most representative evolutionary fuzzy systems for subgroup discovery– obtains precise and interpretable subgroups. However in the...

Subgroup discovery can be defined as a form of supervised inductive learning in which, given a population of individuals and a specific property of individuals in which we are interested, find population subgroups that have the most unusual distributional characteristics with respect to the property of interest. Subgroup discovery algorithms aim at discovering individual rules, which must be re...

Many studies have investigated the lattice structure of fuzzy substructures of algebraic sets such as group and ring. Some important results about modularity and distributivity have been obtained in these studies. In this paper, we first define the notion of (normal) (λ,μ)-L-subgroups on a group and investigate some of their properties. In particular, we discuss the relationships among ordinary...

Nowadays a lot of data is collected in online forums. One of the key tasks is to determine the social structure of these online groups, for example the identification of subgroups within a larger group. We will approach the grouping of individual as a classification problem. The classifier will be based on fuzzy logic. The input to the classifier will be linguistic features and degree of relati...

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.

Given a set S, we show that there is a strict relation between the notion of similarity on S and the one of fuzzy subgroup of transformations in S . Such a relation enables us to extablish a connection between fuzzy subgroups and distances.

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

Let (X,N) be a fuzzy normed space. For each 0 < < 1 and a non-empty subset A of X, we define a natural notion for -farthest points from A and a set-valued map x 7→ Q (A, x), called the fuzzy -farthest point map. Then we will investigate basic properties of the fuzzy -farthest point mapping. In particular, we show that the fuzzy -farthest point map is closable.

In this paper, we show that every selective groupoid induced by a fuzzy subset is a pogroupoid, and we discuss several properties in quasi ordered sets by introducing the notion of a framework.