Generalized Anti Fuzzy Subgroups

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.

In this paper,using A.Rosenfeld [1] definition of fuzzy group,we have tried to establish some independent proof of fuzzy group homomorphism and anti fuzzy group homomorphism.

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.

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.

International Journal of Algebra and Statistics, 2016

More general form of "quasi-coincident with" relation (q) is introduced, and related properties are investigated. The notions of (∈, ∈ ∨ q δ 0)-fuzzy subgroups, q δ 0-level sets and ∈ ∨ q δ 0-level sets are introduced, and related results are investigated. Relations between an (∈, ∈)-fuzzy subgroup and an (∈, ∈ ∨ q δ 0)-fuzzy subgroup are discussed, and characterizations of (∈, ∈ ∨ q δ 0)-fuzzy subgroups are displayed by using level sets and ∈ ∨ q δ 0-level sets. The concepts of ∈ ∨ q δ 0-admissible fuzzy sets, admissible (∈, ∈ ∨ q δ 0)-fuzzy subgroups and δ-characteristic fuzzy sets are introduced. Using these notions, characterizations of admissible (∈, ∈ ∨ q δ 0)-fuzzy subgroups and admissible subgroups are considered. 2010 Mathematics Subject Classification. 20N25, 03E72. Keywords. (∈, ∈ ∨ q δ 0)-fuzzy subgroup, q δ 0-level set, ∈ ∨ q δ 0-admissible fuzzy set.

Advances in Mathematics: Scientific Journal, 2020

An overview of κ-anti fuzzy subgroup of a group is presented and some related basic results are approached in this paper. In addition, the κ-anti fuzzy subgroup of a group is characterized. Moreover some properties of κ-anti fuzzy subgroup under group homomorphism are investigated.

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.

For any intuitionistic multi-fuzzy set A = { < x , µ A (x) , ν A (x) > : x∈X} of an universe set X, we study the set [A] (α, β) called the (α, β)–lower cut of A. It is the crisp multi-set { x∈X : µ i (x) ≤ α i , ν i (x) ≥ β i , ∀i } of X. In this paper, an attempt has been made to study some algebraic structure of intuitionistic multi-anti fuzzy subgroups and their properties with the help of their (α, β)–lower cut sets. Keywords Intuitionistic fuzzy set (IFS), Intuitionistic multi-fuzzy set (IMFS), Intuitionistic multi-anti fuzzy subgroup (IMAFSG), Intuitionistic multi-anti fuzzy normal subgroup (IMAFNSG), (,)–lower cut, Homomorphism.

Discrete Dynamics in Nature and Society

Fuzzy and anti fuzzy normal subgroups are the current instrument for dealing with ambiguity in various decision-making challenges. This article discusses γ -anti fuzzy normal subgroups and γ -fuzzy normal subgroups. Set-theoretic properties of union and intersection are examined and it is observed that union and intersection of γ -anti fuzzy normal subgroups are γ -anti fuzzy normal subgroups. Employee selection impacts the input quality of employees and hence plays an important part in human resource management. The cost of a group is established in proportion to the fuzzy multisets of a fuzzy multigroup. It was a good idea to introduce anti-intuitionistic fuzzy sets and anti-intuitionistic fuzzy subgroups, as well as to demonstrate some of their algebraic features. Product of γ -anti fuzzy normal subgroups and γ -fuzzy normal subgroups is defined, the product’s algebraic nature is analyzed, and the findings are supported by presenting γ -anti typical sections with blurring and γ -...

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.