Bipolar L-fuzzy sub ℓ-HX group with their cosets

Abstract

In this paper, we define  bipolar L-fuzzy cosets of  bipolar L-fuzzy and   bipolar anti L-fuzzy sub ℓ-HX groups. Level subset of bipolar L-fuzzy cosets and lower level subset of bipolar L-fuzzy cosets  also discussed. We define the pseudo bipolar L-fuzzy cosets of  bipolar L-fuzzy and  bipolar anti L-fuzzy sub ℓ-HX group. We also discuss some properties of pseudo bipolar L-fuzzy cosets of bipolar L-fuzzy sub ℓ-HX group using the concepts of  homomorphism and anti homomorphism.