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

• Doctoral Forum • Previous Articles     Next Articles

(∈,∈∨)-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

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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