A Study on Bipolar L-fuzzy Normal Sub?-HX groups

Abstract

In this paper, we define the bipolar L-fuzzy normal sub ?-group of  a ?-group andthe bipolar L-fuzzy normal sub ?-HX group of  a ?-HX group. We discuss some properties of bipolar L-fuzzy normal sub ?-group and also discuss the properties of bipolar L-fuzzy normal sub ?-HX group under the operations of product and intersection.We prove some theorems of bipolar L-fuzzy normal sub ?-HX group using the concepts of  homomorphism and anti homomorphism.