(λ,μ)模糊软环与(λ,μ)模糊软理想
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摘要
针对软集代数结构问题,利用(λ,μ)模糊代数理论,在模糊软集理论的基础上,引入了(λ,μ)模糊软环的概念,讨论了它们的相关性质。同时,将同态与同构应用到(λ,μ)模糊软环中,并建立了模糊软同态下(λ,μ)模糊软环与(λ,μ)模糊软理想对应的定理。
According to the problem of soft set algebra structure,in this paper,the concept of( λ,μ) fuzzy soft rings was introduced by using the theory of( λ,μ) fuzzy algebra based on the theory of fuzzy soft set. Their relevant properties were discussed. At the same time,homomorphism and isomorphism were applied to( λ,μ)fuzzy soft rings,and the corresponding theorems of( λ,μ) fuzzy soft rings and( λ,μ) fuzzy soft ideals under the fuzzy soft homomorphism were established.
According to the problem of soft set algebra structure,in this paper,the concept of( λ,μ) fuzzy soft rings was introduced by using the theory of( λ,μ) fuzzy algebra based on the theory of fuzzy soft set. Their relevant properties were discussed. At the same time,homomorphism and isomorphism were applied to( λ,μ)fuzzy soft rings,and the corresponding theorems of( λ,μ) fuzzy soft rings and( λ,μ) fuzzy soft ideals under the fuzzy soft homomorphism were established.
引文
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[6]刘鑫琳,黎昌珍.直觉梯形模糊数集成算子及在群决策中的应用[J].河南科技大学学报:自然科学版,2014,35(6):88-93.
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[8]Maji P k,Roy A R,Biswas R.Soft Set Theory[J].Computer and Mathematics Application,2003,45(4/5):555-562.
[9]阎瑞霞,刘金良,姚炳学.模糊软集与模糊软群[J].数学的实践与认识,2010,40(8):144-148.
[10]Ebubekir I,Mehmet A O.Fuzzy Soft Rings and Fuzzy Soft Ideals[J].Neural Computing and Applications,2012,21(1):1-8.
[11]Maji P K,Biswas R,Roy A R.Fuzzy Soft Sets[J].The Journal of Fuzzy Mathematics,2001,9(3):589-602.
[12]Ali M I,Feng F,Liu X.et al.On Some New Operations in Soft Set Theory[J].Computer and Mathematics Application,2009,57:1547-1553.
[13]Aygunohlu A,Aygun H.Introduction to Fuzzy Soft Groups[J].Computer and Mathematics Application,2009,58(6):1279-1286.
[14]姚炳学.群与环上的模糊理论[M].北京:科学出版社,2008.
[2]Rosenfeld A.Fuzzy Groups[J].Math Anal Appl,1971,35:512-517.
[3]Bhakat S K,Das P.(∈,∈∨q)Fuzzy Subgroups[J].Fuzzy Sets and Systems,1996,80:359-368.
[4]Yao B.(λ,μ)Fuzzy Normal Subgroups and(λ,μ)Fuzzy Quotient Subgroups[J].The Journal of Fuzzy Mathematics,2005,13(3):695-705.
[5]孙小慧,吴涛,孙恒,等.一种基于区间直觉模糊集的多属性决策方法[J].河南科技大学学报:自然科学版,2013,34(5):87-90.
[6]刘鑫琳,黎昌珍.直觉梯形模糊数集成算子及在群决策中的应用[J].河南科技大学学报:自然科学版,2014,35(6):88-93.
[7]Molodtsov D.Soft Set Theory-first Results[J].Computer and Mathematics Application,1999,37(4/5):19-31.
[8]Maji P k,Roy A R,Biswas R.Soft Set Theory[J].Computer and Mathematics Application,2003,45(4/5):555-562.
[9]阎瑞霞,刘金良,姚炳学.模糊软集与模糊软群[J].数学的实践与认识,2010,40(8):144-148.
[10]Ebubekir I,Mehmet A O.Fuzzy Soft Rings and Fuzzy Soft Ideals[J].Neural Computing and Applications,2012,21(1):1-8.
[11]Maji P K,Biswas R,Roy A R.Fuzzy Soft Sets[J].The Journal of Fuzzy Mathematics,2001,9(3):589-602.
[12]Ali M I,Feng F,Liu X.et al.On Some New Operations in Soft Set Theory[J].Computer and Mathematics Application,2009,57:1547-1553.
[13]Aygunohlu A,Aygun H.Introduction to Fuzzy Soft Groups[J].Computer and Mathematics Application,2009,58(6):1279-1286.
[14]姚炳学.群与环上的模糊理论[M].北京:科学出版社,2008.