SOME CONTRIBUTION ON UPPER NORMAL FUZZY SUBGROUPS

2012

The author have already introduced the notion of -fuzzy set and -anti fuzzy set in a group and studied their properties in [5] and [6] respectively. In this paper, we introduced the notion of ( , )-fuzzy set and subsequently study ( , )-fuzzy subgroup (normal subgroup) and their related properties. We have also obtained a natural homomorphism from the group G to the set of all ( , )-fuzzy cosets of the ( , )-normal subgroup of the group G. Finally, the behaviour of these ( , )-fuzzy subgroups (normal subgroups) under group homomorphism have been discussed.

International Journal of Innovative Research in Engineering & Management, 2018

The purpose of this paper is to discuss the nature of fuzzy level subgroups under homomorphism and anti-homomorphism. It is shown that homomorphic image (pre-image)/anti-homomorphic image (pre-image) of level subgroups is also a level subgroup.

2014

This paper is to further investigate some properties of an anti fuzzy subgroup of a group in relation to pseudo coset. It also uses isomorphism theorems to establish some results in relation to level subgroups of a fuzzy subgroup μ of a group G.

Fuzzy Sets and Systems, 2001

This paper is the third in a series of papers studying equivalence classes of fuzzy subgroups of a given group under a suitable equivalence relation. We introduce the notion of a pinned flag in order to study the operations sum, intersection and union, and their behavior with respect to the equivalence. Further, we investigate the extent to which a homomorphism preserves the equivalence. Whenever the equivalences are not preserved, we have provided suitable counterexamples.

Communications of the Korean Mathematical Society, 2011

Using the "belongs to" relation and "quasi-coincident with" relation between a fuzzy point and a fuzzy subgroup, Bhakat and Das, in 1992 and 1996, initiated general types of fuzzy subgroups which are a generalization of Rosenfeld's fuzzy subgroups. In this paper, more general notions of "belongs to" and "quasi-coincident with" relation between a fuzzy point and a fuzzy set are provided, and more general formulations of general types of fuzzy (normal) subgroups by Bhakat and Das are discussed. Furthermore, general type of coset is introduced, and related fundamental properties are investigated.

IRJET, 2020

Fuzzy group theory has many applications in Physics, chemistry, bio informatics and computer science problems. Applications of fuzzy set theory have also been established in many areas as engineering, medicine, psychology, economics, robotics, etc In this paper the preliminaries required for the concept of Fuzzy subsets, Fuzzy subgroups and properties of fuzzy groups, introduction to the concept of normal fuzzy groups were investigated.

2018

In this paper, we define the notion of o-fuzzy subgroup and investigate the condition under which a fuzzy subgroup is o-fuzzy subgroup. We introduce the notion of o-fuzzy cosets and establish their algebraic properties. We also initiate the study of o-fuzzy normal subgroups and quotient group with respect to o-fuzzy normal subgroup and prove some of their various group theoretic properties.

Thai Journal of Mathematics, 2019

In this paper, proof of some results relating to fuzzy subgroup have been provided. Some new theorems on fuzzy cosets of fuzzy subgroup of a group are also stated and proved.

International Journal of Computer Applications, 2013

In this paper, proofs of some theorems relating to fuzzy subgroups, pseudo fuzzy cosets and pseudo fuzzy double cosets have been provided. Some new theorems are also stated and proved.

International Journal of Scientific Research, 2012

In this paper, we have introduced the concept of Bipolar valued fuzzy subgroup, Bipolar valued fuzzy normal subgroups and investigate some associated results.