(λ,μ)模糊软群与(λ,μ)模糊正规软群
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摘要
针对软集代数结构问题,本文利用(λ,μ)模糊代数理论,在模糊软集理论的基础上,引入了(λ,μ)模糊软群的概念,讨论了它们的相关性质;同时将同态与同构应用到(λ,μ)模糊软群中,并建立了模糊软同态下(λ,μ)模糊软群与(λ,μ)模糊正规软群对应的定理.
According to the problem of soft set algebra's structure,in this paper,the concept of(λ,μ)fuzzy soft groups is introduced by using the theory of(λ,μ)fuzzy algebra based on the theory of fuzzy soft set and their relevant properties are discussed.At the same time,homomorphism and isomorphism are applied to(λ,μ)fuzzy soft groups,the corresponding theorems of(λ,μ)fuzzy soft groups and(λ,μ)fuzzy normal soft groups under the fuzzy soft homomorphism are established.
According to the problem of soft set algebra's structure,in this paper,the concept of(λ,μ)fuzzy soft groups is introduced by using the theory of(λ,μ)fuzzy algebra based on the theory of fuzzy soft set and their relevant properties are discussed.At the same time,homomorphism and isomorphism are applied to(λ,μ)fuzzy soft groups,the corresponding theorems of(λ,μ)fuzzy soft groups and(λ,μ)fuzzy normal soft groups under the fuzzy soft homomorphism are established.
引文
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[3]Bhakat S K,DAS P.(∈,∈∨q)fuzzy subgroup[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]Molodtsov D.Soft set theory-first results[J].Computer and Mathematics with Application,1999,37:19-31.
[6]Maji P K,Biswas R,Roy A R.Fuzzy soft sets[J].The Journal of Fuzzy Mathematics,2001,9(3):589-602.
[7]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.
[8]Yuan X,Zhang C,Ren Y.Generalized fuzzy groups and many-valued implications[J].Fuzzy Sets and Systems,2003,138:205-211.
[9]Aktas H,Cagman N.Soft sets and soft groups[J].Information Sciences,2007,177:2 726-2 735.
[10]Aygunoglu A,Aygun H.Introduction to fuzzy soft groups[J].Computer and Mathematics with Application,2009,58(6):1 279-1286.
[11]Ali M I,Feng F,Liu X.et al.On some new operations in soft set theory[J].Computer and Mathematics with Application,2009,57:1 547-1 553.
[12]Sezgin A,Atagun A O.Soft groups and normalistic soft groups[J].Computer and Mathematics with Application,2011,62:685-698.
[13]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 subgroup[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]Molodtsov D.Soft set theory-first results[J].Computer and Mathematics with Application,1999,37:19-31.
[6]Maji P K,Biswas R,Roy A R.Fuzzy soft sets[J].The Journal of Fuzzy Mathematics,2001,9(3):589-602.
[7]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.
[8]Yuan X,Zhang C,Ren Y.Generalized fuzzy groups and many-valued implications[J].Fuzzy Sets and Systems,2003,138:205-211.
[9]Aktas H,Cagman N.Soft sets and soft groups[J].Information Sciences,2007,177:2 726-2 735.
[10]Aygunoglu A,Aygun H.Introduction to fuzzy soft groups[J].Computer and Mathematics with Application,2009,58(6):1 279-1286.
[11]Ali M I,Feng F,Liu X.et al.On some new operations in soft set theory[J].Computer and Mathematics with Application,2009,57:1 547-1 553.
[12]Sezgin A,Atagun A O.Soft groups and normalistic soft groups[J].Computer and Mathematics with Application,2011,62:685-698.
[13]姚炳学.群与环上的模糊理论[M].北京:科学出版社,2008.