(∈,∈∨q)-模糊正规化子与(∈,∈∨q)-模糊商子群  

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

作　　者：姚炳学[1] 

机构地区：[1]聊城大学数学与系统科学系,山东聊城252059

出　　处：《吉首大学学报（自然科学版）》2003年第2期23-25,34,共4页Journal of Jishou University(Natural Sciences Edition)

基　　金：山东省自然科学基金资助项目(Y2000A05)

摘　　要：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.

关 键 词：(∈ ∈∨q)-模糊子群 (∈ ∈∨q)-模糊正规化子 (∈ ∈∨q)-模糊中心化子 (∈ ∈∨q)-模糊商群 (∈ ∈∨q)-模糊商子群 模糊子集 模糊数学 

分 类 号：O159[理学—数学] O152[理学—基础数学]