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...

Quite a few problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made under uncertainty. In this paper, we focus on Fuzzy nonlinear optimization problems in the Linear Fuzzy Real (LFR) numbers. The problems will consist of fuzzy constraints and objective functions, crisp constraints with a fuzzy objective function, o...

In this paper, we further study properties of fuzzy almost continuous functions in Singal’s and Hussain’s sense and establish a condition for their equivalence which is an improvement of Theorem 5.5 of [2]. Some divergences from straightforward fuzzification of General Topology have also been noted in Example 1 and Theorem 4. We also define fuzzy almost weakly continuous and fuzzy nearly almost...

Department of Mathematics, Jadavpur University Kolkata-700032, India manasi−[email protected] Abstract The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of Γsemigroups in order to obtain some characterization theorems. We also introduce the not...

In this paper, we characterize ordered semigroups in terms of fuzzy quasi-ideals. We characterize left simple, right simple and completely regular ordered semigroups in terms of fuzzy quasi-ideals. We define semiprime fuzzy quasi-ideal of ordered semigroups and characterize completely regular ordered semigroup in terms of semiprime fuzzy quasi-ideals. We also study the decomposition of left and...

As a generalization of a fuzzy finite state machine, the notion of a bipolar fuzzy finite state machine is introduced. Also, the concepts of a bipolar (immediate) successor, a bipolar exchange property and a bipolar subsystem are introduced. Some related properties are discussed. A condition for a bipolar fuzzy finite state machine to satisfy the bipolar exchange property is established. A char...

In this paper we present some definitions which are the natural combination of the definition of asymptotic equivalence, statistical convergence, lacunary statistical convergence of fuzzy real numbers and ideal. In addition, we also present asymptotically ideal equivalent sequences of fuzzy real numbers and establish some relations related to this concept. Finally we introduce the notion of Ces...

In the present communication, three new divergence measures between fuzzy sets are proposed. The validity of these divergence measures is examined axiomatically. Relation of the proposed divergence measures with the cardinality of a universe of discourse is established. Some properties of these divergence measures are established. Relation of divergence between fuzzy sets with aggregation opera...

In this paper we highlight the specific meaning of images of fuzzy sets under fuzzy relations in the context of fuzzy topology. More precisely we show that fuzzy modifiers taking direct and superdirect images of fuzzy sets under fuzzy pre-orderings are respectively closure and interior operators, inducing fuzzy topologies. Furthermore we investigate under which conditions the same applies to th...

This paper presents, by means of Alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces, a systematic investigation of the interrelationship between fuzzy preordered sets, topological spaces, and fuzzy topological spaces. © 2006 Elsevier B.V. All rights reserved.