(∈,∈∨q)-模糊正规化子与(∈,∈∨q)-模糊商子群

(∈,∈∨q)-Fuzzy Normalizer and (∈,∈∨q)-Fuzzy Quotient Subgroup

在(∈,∈∨q)-模糊子群的基础上,引入了(∈,∈∨q)-模糊正规化子与(∈,∈∨q)-模糊中心化子的概念,并讨论了它们的一些性质.同时,给出了(∈,∈∨q)-模糊商群与(∈,∈∨q)-模糊商子群的定义,建立了(∈,∈∨q)-模糊商群的同构定理.

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.