J4 ›› 2011, Vol. 24 ›› Issue (5): 49-51.

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The (∈,∈∨q)- fuzzy bi-ideals of Γ- semigroups

 YANG Guang, XU Xin-Zhai, LI Nan   

  1. School of Mathematics, Shandong Normal University, Jinan 250014,China
  • Received:2011-04-11 Published:2011-10-20 Online:2011-10-20

Abstract:

       We generalize the concepts of some (∈,∈∨q)- fuzzy subsets to Γ- semigroups. We also introduce the concept of (∈,∈∨q)- fuzzy Γ- subsemigroup,(∈,∈∨q)- fuzzy bi-ideal and (∈,∈∨q)- fuzzy generalized bi-ideal into Γ- semigroups, and address their expressions with some theories of fuzzy sets. It is proved that the intersection and union of (∈,∈∨q)- fuzzy bi-ideals are still (∈,∈∨q)- fuzzy bi-ideals, and that every (∈,∈∨q)- fuzzy generalized bi-ideal of regular Γ- semigroups is a (∈,∈∨q)- fuzzy bi-ideal.

Key words: Γ-semigroup, (∈, ∈∨q)-fuzzy bi-ideals, fuzzy point

CLC Number: 

  • O152.7

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