• BIPOLAR ANTI-FUZZY NORMAL HX SUBGROUPS

Abstract

In this paper, we define a new algebraic structure of a bipolar anti fuzzy normal HX subgroup and some properties of intersection and union bipolar anti fuzzy normal HX subgroups are discussed. We establish the necessary condition for intersection of any two bipolar anti fuzzy normal HX subgroups is a bipolar anti fuzzy normal HX subgroup.The concept of an anti image, anti pre-image of a bipolar fuzzy subsets were discuss in detail a series of homomorphic and anti homomorphic properties of bipolar anti fuzzy normal HX subgroups. We define lower level subset of a bipolar anti fuzzy normal HX subgroup and discuss some of its properties. Characterizations of lower level subsets of a bipolar anti fuzzy normal HX subgroup of a HX group are given.