Abstract: Based on the concept of (∈，∈∨ｑ)-fuzzy subgroup introduced by S.K.Bhakat in 1992,the notions of  (∈，∈∨ｑ)- fuzzy normalizer and (∈，∈∨ｑ)-fuzzy centralizer are introduced.Some properties of (∈，∈∨ｑ)-fuzzy normalizer and (∈，∈∨ｑ)- fuzzy centralizer are discussed.Then,the definition of(∈，∈∨ｑ)- fuzzy quotient group and (∈，∈∨ｑ)-fuzzy quotient subgroup is given.At last,the isomorphism theorem for (∈，∈∨ｑ)-fuzzy quotient group is established.The main results include:(1)if is a fuzzy subset of,then the (∈，∈∨ｑ)-fuzzy normalizer of is a subgroup of;(2)if is a fuzzy subgroup of,then the (∈，∈∨ｑ)-fuzzy centralizer of is a subgroup of and a normal subgroup of;(3)if and are (∈，∈∨ｑ)-fuzzy normal subgroup and (∈，∈∨ｑ)-fuzzy subgroup of,respectively,then is a (∈，∈∨ｑ)-fuzzy subgroup of.

Key words: (∈, ∈∨ｑ)-fuzzy subgroup；(∈, ∈∨ｑ)-fuzzy normal subgroup；(∈, ∈∨ｑ)-fuzzy normalizer；(∈, ∈∨ｑ)-fuzzy centralizer；(∈, ∈∨ｑ)-fuzzy quotient subgroup