Κ-Anti-Fuzzy 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.

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.

Journal of Inequalities and Applications, 2012

We introduced the notions of (l, μ)-anti-fuzzy subgroups, studied some properties of them and discussed the product of them.

Computers, Materials & Continua

Recently, fuzzy multi-sets have come to the forefront of scientists' interest and have been used in algebraic structures such as multi-groups, multirings, anti-fuzzy multigroup and (α, γ)-anti-fuzzy subgroups. In this paper, we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as (α, γ)-anti-multi-fuzzy subgroups. In a way, the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group. The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group. The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view. Therefore, in this paper, we define (α, γ)-antimulti-fuzzy subgroups, (α, γ)-anti-multi-fuzzy normal subgroups, (α, γ)-antimulti-fuzzy homomorphism on (α, γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures. Then, we introduce the concept (α, γ)-anti-multi-fuzzy subgroups and (α, γ)-anti-multi-fuzzy normal subgroups and of their properties. This new concept of homomorphism as a bridge among set theory, fuzzy set theory, anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure. Certain results that discuss the (α, γ) cuts of anti-fuzzy multigroup are explored.

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 Computer Applications, 2010

In this paper, we define the algebraic structures of anti Q-fuzzy subgroup and some related properties are investigated. The purpose of this study is to implement the fuzzy set theory and group theory in anti-Q fuzzy subgroups. Characterizations of lower level subsets of an anti-Q fuzzy subgroup of a group are given.

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.

International Journal of Computer Applications, 2010

In this paper, we made an attempt to study the algebraic nature of anti fuzzy sub-bigroup of a bigroup and anti fuzzy sub-bigroup of a group and discussed some of its properties with counter example.

2012

As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by K. T. Atanassov in 1986. In this article, we study the upper �-level cut and lower �-level cut of intuitionistic fuzzy sets in a group. Also we study some properties of intuitionistic anti-fuzzy subgroups of a group and prove some characterizations for intuitionistic anti-fuzzy subgroups.

As an abstraction of the geometric notion of translation, we introduce two operators T � + and T � -called the fuzzy translation operator on the fuzzy set A. We investigate their properties and also study their action on Anti fuzzy subgroups (Anti fuzzy normal subgroups) of a group and show that they are invariant under these translation. However we show that anti fuzzy abelianness is not translation invariant. We also study the interaction of these operators with anti fuzzy coset formation and prove that operators commute.