A new approach to the fuzzification of groups

In the present paper we present a new approach to the fuzzification of groups, which is defined by the hazy associative law (a new fuzzy associative law) on hazy binary operations. It is also called an M-hazy group. The basic idea is to generalize the binary operation of classical algebras to fuzzy binary operation. Some properties of M-hazy groups and M-hazy subgroups are discussed. Besides, we also study the homomorphisms between two M-hazy groups.