Some properties of upper fuzzy order

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.

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.

2013

On the basis of fuzzy sets introduced by L.A. Zadeh, we first gave the definition of fuzzy set and then defined fuzzy subgroups and fuzzy normal subgroups and finally, defined quotient group of the fuzzy cosets of an fuzzy normal subgroup. This paper proves a necessary and sufficient condition of -fuzzy subgroup (normal subgroup) to be fuzzy subgroup (normal subgroup). Some properties of quotient group of -fuzzy normal subgroups are also discussed.

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.

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.

2011

Multi-fuzzy set theory is an extension of fuzzy set theory, which deals with the multi dimensional fuzziness. In this paper we introduce the concepts of multi-fuzzy subgroups and normal multi-fuzzy subgroups. Mathematics Subject Classification: MSC: 20N25; 03E72; 08A72

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.

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.

International Journal of Computer Applications, 2010

The theory of fuzzy sets has developed in many directions and is finding applications in a wide variety of fields. Resentful in 1971 used this concept to develop the theory of fuzzy groups in this paper we have given independent proof of several theorems on fuzzy groups. We discuss about Fuzzy groups and investigate some of their structures on the concept of Fuzzy Group family and L-fuzzy number.

2018

In this paper, we initiate the study of o-anti fuzzy subgroup and prove that every anti fuzzy subgroup is o-anti fuzzy subgroup. We introduce the notion of o-anti fuzzy cosets and establish their algebraic properties. We also define o-anti fuzzy normal subgroup and quotient group with respect to this particular group and prove some of it’s various group theoretic properties.