journal6 ›› 2003, Vol. 24 ›› Issue (2): 23-25.

• 博士论坛 • 上一篇    下一篇

(∈,∈∨)-模糊正规化子与(∈,∈∨)-模糊商子群

  

  1. (聊城大学数学与系统科学系,山东 聊城252059)
  • 出版日期:2003-06-15 发布日期:2012-11-07
  • 作者简介:姚炳学(1963-),男,山东省诸城人,博士,聊城大学数学与系统科学系教授,主要从事模糊代数理论研究.
  • 基金资助:

    山东省自然科学基金资助项目(Y2000A05)

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

  1. (Department of Mathematics and System Science,Liaocheng University,Liaocheng 252059,Shandong China)
  • Online:2003-06-15 Published:2012-11-07

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.

关键词: (&isin, &isin, &or, q)-子群, (&isin, &isin, &or, q)-模糊正规子群, (&isin, &isin, &or, q)-模糊正规化子, (&isin, &isin, &or, q)-模糊中心化子, (&isin, &isin, &or, q)-模糊商子群

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

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