The main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group. By using a similar method, some important steps in counting the number of fuzzy subgroups of a finite elementary abelian p-group are also made. © 2007 Elsevier B.V. All rights reserved. MSC: primary 20N2503E72; secondary 20K0120D30

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...

There are various types of generalizations of fuzzy continuous functions in the development of fuzzy topology. Recently some decompositions of fuzzy continuity have been obtained by various authors with the help of generalized fuzzy continuous functions in fuzzy topological spaces. In this paper we obtain decomposition of fuzzy continuity by using a new generalized fuzzy continuity in fuzzy top...

Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completen...

In this paper a first step in classifying the fuzzy subgroups of a finite nonabelian group is made. We develop a general method to count the number of distinct fuzzy subgroups of such groups. Explicit formulas are obtained in the particular case of dihedral groups.

Park et al. (2011) introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with res...

In this paper we introduce intuitionistic fuzzy almost generalized semi-pre closed mappings and intuitionistic fuzzy almost generalized semi-pre open mappings. We investigate some of their properties. Also we provide the relation between intuitionistic fuzzy almost generalized semi-pre closed mappings and other intuitionistic fuzzy closed mappings.

One of the most important problems of fuzzy group theory is to classify the fuzzy subgroups of a finite group. This topic has enjoyed a rapid development in the last few years. Several papers have treated the particular case of finite abelian groups. Thus, in [13] the number of distinct fuzzy subgroups of a finite cyclic group of square-free order is determined, while [14–16] and [28] deal with...