A new view of L-fuzzy polygroups

In this paper, we introduce the concept of (weak) L-fuzzy polygroups and give a theorem to present the connection between the crisp polygroups and L-fuzzy polygroups. We also provide the notion of (normal) L-fuzzy subpolygroups of a (weak) L-fuzzy polygroup and investigate some of their properties. We show that the set of all the normal L-fuzzy subpolygroups is a modular lattice and obtain a kind of weak L-fuzzy quotient polygroup. Moreover, we define two kinds of operators on L(H), where L (H) is the set of all the L-fuzzy subsets in a weak L-fuzzy polygroup H, to characterize L-fuzzy subpolygroups and present some related theorems. Finally, we investigate the homomorphism properties of L-fuzzy polygroups.