L-fuzzy子格上L-fuzzy素理想的研究
|
摘要
在值格为完全分配格的条件下,给出了模糊子格上模糊素理想的定义,借助模糊子集的水平截集,得到了模糊子格上模糊素理想的几种等价刻画形式,同时还研究了模糊素理想的几个相关的性质,在模糊子格上得到的一系列结果具有更一般性的意义。
Under the condition of completely distributive lattice,we present a the definition of L-fuzzy prime ideals of L-fuzzy sublattice.Then with the tool of level sets,we give several equivalent characterizations of L-fuzzy prime ideals.Furthermore,we study some of its properties.All the results on L-fuzzy sublattice will be of more general senses.
Under the condition of completely distributive lattice,we present a the definition of L-fuzzy prime ideals of L-fuzzy sublattice.Then with the tool of level sets,we give several equivalent characterizations of L-fuzzy prime ideals.Furthermore,we study some of its properties.All the results on L-fuzzy sublattice will be of more general senses.
引文
[1]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8:338~353.
[2]Birkhoff G.Lattice theory[M].Amer.Math.Soc.Colloq.publ.,1967.
[3]Goguen J A.L-fuzzy sets[J].J.Math Anal.Appl.,1967,18:145~174.
[4]Sanchez E.Resolution of complsite fuzzy relation equation[J].Inform.And Control,1976,30:38~48.
[5]刘溶滨.Fuzzy子格的代数性质探讨[J].四川师范大学学报,1987,(1):36~39.
[6]Yuan B,Wu W.Fuzzy ideals on a distributive latticed].Fuzzy Sets and System,1990,35:231~240.
[7]Ajmal N,Thomas K V.Fuzzy lattices[J].Information Sciences,1994,79:271~291.
[8]Attallah M.Completely fuzzy prime ideals of distributive lattices[J].The Journal of Fuzzy Mathematics,2000,8(1):151~156.
[9]杨云.格的L-fuzzy理想的代数性质[J].模糊系统与数学,2001,15(1):81~84.
[10]Koguep B B N,Nkuimi C,Lele C.On fuzzy prime ideals of latticed].SJPAM.2008,3,1~11.
[11]吴广庆.格的L-fuzzy素理想[J].模糊系统与数学,2008,22(4):62~67.
[12]刘银萍,辛小龙.模糊子格与模糊子格上的模糊理想[J].模糊系统与数学,2014,28(1);39~45.
[13]史福贵.L_β集合套与L_α集合套理论及应用[J].模糊系统与数学,1995,9(4):65~72.
[14]王国俊.L-fuzzy拓扑空间论[M].西安:陕西师范大学出版社,1988.
[15]盛德成.抽象代数[M].北京:科学出版社,2000.
[16]Kumar R.Fuzzy algebra[M].University of Delhi,1993.
[2]Birkhoff G.Lattice theory[M].Amer.Math.Soc.Colloq.publ.,1967.
[3]Goguen J A.L-fuzzy sets[J].J.Math Anal.Appl.,1967,18:145~174.
[4]Sanchez E.Resolution of complsite fuzzy relation equation[J].Inform.And Control,1976,30:38~48.
[5]刘溶滨.Fuzzy子格的代数性质探讨[J].四川师范大学学报,1987,(1):36~39.
[6]Yuan B,Wu W.Fuzzy ideals on a distributive latticed].Fuzzy Sets and System,1990,35:231~240.
[7]Ajmal N,Thomas K V.Fuzzy lattices[J].Information Sciences,1994,79:271~291.
[8]Attallah M.Completely fuzzy prime ideals of distributive lattices[J].The Journal of Fuzzy Mathematics,2000,8(1):151~156.
[9]杨云.格的L-fuzzy理想的代数性质[J].模糊系统与数学,2001,15(1):81~84.
[10]Koguep B B N,Nkuimi C,Lele C.On fuzzy prime ideals of latticed].SJPAM.2008,3,1~11.
[11]吴广庆.格的L-fuzzy素理想[J].模糊系统与数学,2008,22(4):62~67.
[12]刘银萍,辛小龙.模糊子格与模糊子格上的模糊理想[J].模糊系统与数学,2014,28(1);39~45.
[13]史福贵.L_β集合套与L_α集合套理论及应用[J].模糊系统与数学,1995,9(4):65~72.
[14]王国俊.L-fuzzy拓扑空间论[M].西安:陕西师范大学出版社,1988.
[15]盛德成.抽象代数[M].北京:科学出版社,2000.
[16]Kumar R.Fuzzy algebra[M].University of Delhi,1993.