Interval-valued Fuzzy Subgroups Research Articles

A NEW VIEW OF FUZZY ORDERED SEMIGROUPS

fuzzy coding theory, fuzzy finite state machines, and fuzzy languages. In this paper, we introduce the concept of an interval-valued -fuzzy filter of an ordered semigroup, where with. Since the concept of an interval-valued -fuzzy filter is an important and useful generalization of the ordinary interval-valued fuzzy filter, we discuss some fundamental aspects of an interval-valued -fuzzy filters. An interval-valued -fuzzy filter is a generalization of the existing concept of an interval-valued fuzzy filter. We discuss the concept of an interval-valued -fuzzy left (right)-filters and provide some characterization theorems. Finally, we extend the concept of an interval-valued fuzzy subgroup with thresholds to the concept of an interval-valued fuzzy left (right)-filter with thresholds of s.

Lattices of Interval-Valued Fuzzy Subgroups

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.

INTERVAL-VALUED FUZZY SUBGROUPS

We study the conditions under which a given interval-valued fuzzy subgroup of a given group can or can not be realized as a union of two interval-valued fuzzy proper subgroups. Moreover, we provide a simple necessary and su cient condition for the unio of an arbitrary family of interval-valued fuzzy subgroups to be an interval-valued fuzzy subgroup. Also we formulate the concept of interval-valued fuzzy subgroup generated by a given interval-valued fuzzy set by level subgroups. Furthermore we give characterizations of interval-valued fuzzy conjugate subgroups and interval-valued fuzzy characteristic subgroups by their level subgroups. Also we investigate the level subgroups of the homomorphic image of a given interval-valued fuzzy subgroup.

INTERVAL-VALUED FUZZY SUBGROUPS AND LEVEL SUBGROUPS

We introduce the concept of level subgroups of an interval-valued fuzzy subgroup and study some of its properties. These level subgroups in turn play an important role in the characterization of all interval-valued fuzzy subgroup of a prime cyclic group.

Interval-Valued Fuzzy Cosets

First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups. Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

INTERVAL-VALUED FUZZY SUBGROUPS AND HOMOMORPHISMS

We obtain the interval-valued fuzzy subgroups generated by interval-valued fuzzy sets and some properties preserved by a ring homomorphism. Furthermore, we introduce the concepts of interval-valued fuzzy coset and study some of it's properties.

INTERVAL-VALUED FUZZY SUBGROUPS AND RINGS

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.

T-INTERVAL-VALUED FUZZY SUBGROUPS AND RINGS

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.

The [formula omitted]-interval-valued fuzzy subgroup

In this paper, the idempotent interval conorm S H induced by a T-conorm on the space of the interval-valued fuzzy sets on groups is introduced, the S H -interval-valued fuzzy subgroup is defined. In the meantime, some of its basic properties and structural characteristics are discussed and studied. Furthermore, the theorems of the homomorphic image and the inverse image are given.

Rosenfeld's fuzzy subgroups with interval-valued membership functions

In this paper we define interval-valued fuzzy subgroups (i.e. i–v fuzzy subgroups) of Rosenfeld's nature. A necessary and sufficient condition for an i–v fuzzy subset to be an i–v fuzzy subgroup is stated. Intersection of two i–v fuzzy subgroups is also an i–v fuzzy subgroup. The images and inverse-images of i–v fuzzy subgroups are defined; and how the images or inverse-images of i–v fuzzy subgroups become i–v fuzzy subgroups is studied.