半群中的(∈,∈∨q)-模糊素理想
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摘要
在(∈,∈∨q)-模糊子群概念的基础上,引入半群中(∈,∈∨q)-模糊理想与(∈,∈∨q)-模糊素理想的概念,研究了它们的特征性质,并给出了若干等价条件.
Based on the concept of(∈,∈∨q)-fuzzy subgroup of a group,the concepts of(∈,∈∨q)-fuzzy ideal and(∈,∈∨q)-fuzzy prime ideal of a semigroup were introduced.Some properties of(∈,∈∨q)-fuzzy ideal and(∈,∈∨q)-fuzzy prime ideal were discussed.At last,several equivalence conditions were established.
Based on the concept of(∈,∈∨q)-fuzzy subgroup of a group,the concepts of(∈,∈∨q)-fuzzy ideal and(∈,∈∨q)-fuzzy prime ideal of a semigroup were introduced.Some properties of(∈,∈∨q)-fuzzy ideal and(∈,∈∨q)-fuzzy prime ideal were discussed.At last,several equivalence conditions were established.
引文
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[2]Rosenfeld A.Fuzzy groups[J].Math.Anal.Appl.,1971,35:512~517.
[3]Kuroki N.On fuzzy ideals and fuzzy bi-ideals in semigroups[J].Fuzzy Set sand Systems,1981,5:203~215.
[4]Kuroki N.Fuzzy semiprime ideals in semigroups[J].Fuzzy Set sand Systems,1982,8:71~79.
[5]Bhakat S K,DasP.(∈,∈∨q)-fuzzy subgroup[J].Fuzzy Setsand Systems,1996,80:359~368.
[6]Bhakat S K,Das P.Fuzzy subrings and ideals redefined[J].Fuzzy Sets and Systems,1996,81:383~393.
[7]Yuan X,Zhang C,Ren Y.Generalized fuzzy groups and many-valued implications[J].Fuzzy Set sand Systems,2003,138:205~211.
[8]袁学海,冯艳萍,刘新,等.(β,α)-模糊子群[J].辽宁师范大学学报(自然科学版),2003,26(1):1~4.
[9]袁学海,冯艳萍,王岚,段瑞霞.(∈,∈∨q)-模糊子群的水平子群[J].辽宁师范大学学报(自然科学版),2005,28(3):270~272.
[10]姚炳学,孙玉真,张诚一.半群中的(λ,μ)-模糊素理想与(λ,μ)-模糊准素理想[J].模糊系统与数学,2010,24(5):31~36.
[2]Rosenfeld A.Fuzzy groups[J].Math.Anal.Appl.,1971,35:512~517.
[3]Kuroki N.On fuzzy ideals and fuzzy bi-ideals in semigroups[J].Fuzzy Set sand Systems,1981,5:203~215.
[4]Kuroki N.Fuzzy semiprime ideals in semigroups[J].Fuzzy Set sand Systems,1982,8:71~79.
[5]Bhakat S K,DasP.(∈,∈∨q)-fuzzy subgroup[J].Fuzzy Setsand Systems,1996,80:359~368.
[6]Bhakat S K,Das P.Fuzzy subrings and ideals redefined[J].Fuzzy Sets and Systems,1996,81:383~393.
[7]Yuan X,Zhang C,Ren Y.Generalized fuzzy groups and many-valued implications[J].Fuzzy Set sand Systems,2003,138:205~211.
[8]袁学海,冯艳萍,刘新,等.(β,α)-模糊子群[J].辽宁师范大学学报(自然科学版),2003,26(1):1~4.
[9]袁学海,冯艳萍,王岚,段瑞霞.(∈,∈∨q)-模糊子群的水平子群[J].辽宁师范大学学报(自然科学版),2005,28(3):270~272.
[10]姚炳学,孙玉真,张诚一.半群中的(λ,μ)-模糊素理想与(λ,μ)-模糊准素理想[J].模糊系统与数学,2010,24(5):31~36.