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

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Γ-半群的(∈,∈∨q)-模糊双理想

 杨光, 许新斋, 李囡   

  1. 山东师范大学数学科学学院,山东 济南 250014
  • 收稿日期:2011-04-11 出版日期:2011-10-20 发布日期:2011-10-20
  • 通信作者: 许新斋 (1953-), 男, 教授, 研究方向为半群的代数理论。 E-mail:xinzhaixu2007@yahoo.cn
  • 作者简介:杨光 (1985-),男, 硕士研究生, 研究方向为半群的代数理论。Email: yangguangsdn@163.com

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 Online:2011-10-20 Published:2011-10-20

摘要:

       将半群中的几种(∈,∈∨q)-模糊子集的概念推广到Γ-半群中,在Γ-半群中引入(∈,∈∨q)-模糊Γ-子半群、(∈,∈∨q)-模糊双理想、(∈,∈∨q)-模糊广义双理想的概念, 用有关模糊集的理论讨论了它们的刻画。证明了(∈,∈∨q)-模糊双理想的交、并仍为(∈,∈∨q)-模糊双理想,正则Γ-半群的每个(∈,∈∨q)-模糊广义双理想为(∈,∈∨q)-模糊双理想。

关键词: &Gamma, -半群, (&isin, &isin, &or, q)-模糊双理想, 模糊点

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

中图分类号: 

  • O152.7