A Certain Class of t-Intuitionistic Fuzzy Subgroups

Muhammad Gulzar,Muhammad Haris Mateen,Nasreen Kausar,Dilshad Alghazzawi

doi:10.1109/access.2020.3020366

Abstract

In this study, the t-intuitionistic fuzzy normalizer and centralizer of t intuitionistic fuzzy subgroup are proposed. The t-intuitionistic fuzzy centralizer is normal subgroup of t-intuitionistic fuzzy normalizer and investigate various algebraic properties of this phenomena. We also introduce the concept of t-intuitionistic fuzzy Abelian and cyclic subgroups and prove that every t-intuitionistic fuzzy subgroup of Abelian (cyclic) group is t-intuitionistic fuzzy Abelian (cyclic) subgroup. We show that the image and pre-image of t-intuitionistic fuzzy Abelian (cyclic) subgroup are t-intuitionistic fuzzy Abelian (cyclic) subgroup under group homomorphism.

Highlights

Camille Jordan named Abelian group due to the pioneer work of Norwegian mathematician Niels Henrik Abel, because Abel established the commutativity of the groups interprets that the roots of the polynomial could be evaluated by using radicals
We introduce the idea of t-intuitionistic fuzzy Abelian subgroups and t-intuitionistic fuzzy cyclic subgroups and prove that every t-intuitionistic fuzzy subgroup of Abelian group is t-intuitionistic fuzzy Abelian subgroup
ABELIAN SUBGROUPS This section devoted to study of t-IFASG (t-IFCSG) subgroup under group homomorphism and show that homomorphic image and pre-image of t-IFASG (t-IFCSG) form a t-IFASG (t -IFCSG)

Summary

INTRODUCTION

Camille Jordan named Abelian group due to the pioneer work of Norwegian mathematician Niels Henrik Abel, because Abel established the commutativity of the groups interprets that the roots of the polynomial could be evaluated by using radicals. T-intuitionistic fuzzy set (t-IFS) At of P is an object triplet of the form At = {< x, μAt (w), νAt (w) >: w ∈ P}, where μAt : P → [0, 1] and νAt : P → [0, 1] define the degree of membership and degree of non-membership of the element w ∈ P, respectively, these functions must be satisfied the condition 0 μAt (w) + νAt (w) 1. Definition 2.4 [18]: A t-IFSG A = (μAt , νAt ) of a group G is said to be t-intuitionistic fuzzy normal subgroup (t-IFNSG) of G if. The set C(At ) = {a ∈ G : μAt ([a, w])} = μAt (e) and νAt ([a, w]) = νAt (e), for all w ∈ G} is called t-intuitionistic fuzzy centralizer of At in G, where [a, w] is the commutator of the two elements a and w in G, i.e., [a, w] = a−1w−1aw. At is t-IFCSG of G but G is not cyclic group

HOMOMORPHISM OF t -INTUITIONISTIC FUZZY

CONCLUSION