• BIPOLAR FUZZY HX GROUP AND ITS LEVEL SUB HX GROUPS

Abstract

In this paper, we define the concept of a bipolar fuzzy HX group and define a new algebraic structure of a bipolar fuzzy sub HX group of a HX group and level sub HX group of a HX group and some related properties are investigated. The purpose of this study is to implement the fuzzy set theory and group theory in bipolar fuzzy sub HX group of a HX group. Characterizations of level subsets of a bipolar fuzzy sub HX group of a HX group are given. we also discussed the relation between a given a bipolar  fuzzy sub HX group of a HX group and its  level sub HX groups and investigate the conditions under which a given HX group has a properly inclusive chain of sub HX groups. In particular, we formulate how to structure a bipolar fuzzy sub HX group of a HX group by a given chain of sub HX groups. We also establish the relation between bipolar fuzzy HX group and bipolar anti fuzzy HX group of a HX group.