格蕴涵代数的Ω-直觉模糊LI-理想
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摘要
给定一个集合Ω,将Ω-直觉模糊集与格蕴涵代数相结合,给出了Ω-直觉模糊LI-理想的概念,并研究了其相关性质;讨论了Ω-直觉模糊LI-理想与Ω-模糊LI-理想之间的关系,得到了一些等价刻画。
Let Ω be a set.By combining the Ω-intuitionistic fuzzy sets and the the lattice implication algebras,the concept of Ω-intuitionistic fuzzy LI-ideals is proposed,and some related properties are investigated.The relationship between Ω-intuitionistic fuzzy LI-ideals and Ω-fuzzy LI-ideals in the lattice implication algebras is also discussed,and then we obtain some equivalent characterizations.
Let Ω be a set.By combining the Ω-intuitionistic fuzzy sets and the the lattice implication algebras,the concept of Ω-intuitionistic fuzzy LI-ideals is proposed,and some related properties are investigated.The relationship between Ω-intuitionistic fuzzy LI-ideals and Ω-fuzzy LI-ideals in the lattice implication algebras is also discussed,and then we obtain some equivalent characterizations.
引文
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[7]Qin K Y,Xu Y,Si C,Jun Y B Chinju.Ultra LI-ideals in lattice implication algebras[J].Czechoslovak Mathematical Journal,2002,52(127):463~468.
[8]Liu Y L,Liu S Y,Xu Y.ILI-ideals and prime LI-ideals in lattice implication algebra[J].Information Sciences,2003,155(1/2):157~175.
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[17]Pu P M,Liu Y M.Fuzzy topology(I)Neighborhood structure of a fuzzy point and Moore-Smith convergence[J].Journal of Mathematical Analysis And Applications,1980,76(2):571~599.
[18]Pu P M,Liu Y M.Fuzzy topology(II)product and quotient spaces[J].Journal of Mathematical Analysis And Applications,1980,77(1):20~37.
[19]潘玲等.环的(∈,∈∨q)-直觉模糊理想[J].山东大学学报(理学版),2012,47(8):16~21,27.
[20]罗晓棠等.直觉模糊完全正则子半群及其同态[J].模糊系统与数学,2013,27(6):52~58.
[21]裴峥.格蕴涵代数中的直觉模糊滤子[J].西华大学学报(自然科学版),2007,26(2):17~20.
[22]许伟涛,徐扬,潘小东.格蕴涵代数中的直觉模糊关联滤子[J].江南大学学报(自然科学版),2009,8(6):736~739.
[23]朱华,赵建彬,徐扬.格蕴涵代数中的直觉模糊理想[J].模糊系统与数学,2014,28(1):23~27.
[2]徐扬.格蕴涵代数[J].西南交通大学学报,1993,28(1):20~27.
[3]Xu Y,Ruan D,Qin K Y.Lattice-valued logic[M].Berlin:Springer-Verlag,2003.
[4]Jun Y B,Roh E H,Xu Y.LI-ideals in lattice implication algebras[J].Bulletin Korean Mathematical Society,1998,5(1):13~24.
[5]Jun Y B,Xu Y,Qin K Y.Positive implicative and associative ideals of lattice implication algebras[J].Bu11.Korean Math.Soc,1998,1(35):53~61.
[6]Zhao G F,Xu Y,Song Z M.Implicative and fuzzy implicative ideals of lattice implication algebras[J].Chinese Quarterly Journal of Mathematics,2001,16(4):105~110.
[7]Qin K Y,Xu Y,Si C,Jun Y B Chinju.Ultra LI-ideals in lattice implication algebras[J].Czechoslovak Mathematical Journal,2002,52(127):463~468.
[8]Liu Y L,Liu S Y,Xu Y.ILI-ideals and prime LI-ideals in lattice implication algebra[J].Information Sciences,2003,155(1/2):157~175.
[9]Jun Y B.On n-fold implicative ideals of lattice implication algebras[J].Internat.J.Math&Math.Sci.,2001,24(4):695~699.
[10]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8(3):338~353.
[11]Rosenfeld A.Fuzzy groups[J].Journal of Mathematical Analysis and Applications,1971,35:512~517.
[12]Zadeh L A.The concepts of a linguistic variable and its application to approximate reasoning(I)(II)(III)[J].Information Sciences,1975,8(3):199~249;1975,8(4):301~357;1975,9(1):43~80.
[13]Liao Z H,Gu H.fuzzy normal subgroup[J].Fuzzy Systems and Mathematics,2006,20(5):38~43.
[14]Young B J,Kyung H K,Zhang Q.OnΩ-fuzzy ideals of BCK/BCI-algebras[J].The Journal of Fuzzy Mathematics,2001,9(1):173~180.
[15]Atanassow K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87~96.
[16]Yuan X H,Li H X,Lee E S.On the definition of the intuitionistic fuzzy subgroups[J].Computers and Mathematics with Applications,2010,59:3117~3129.
[17]Pu P M,Liu Y M.Fuzzy topology(I)Neighborhood structure of a fuzzy point and Moore-Smith convergence[J].Journal of Mathematical Analysis And Applications,1980,76(2):571~599.
[18]Pu P M,Liu Y M.Fuzzy topology(II)product and quotient spaces[J].Journal of Mathematical Analysis And Applications,1980,77(1):20~37.
[19]潘玲等.环的(∈,∈∨q)-直觉模糊理想[J].山东大学学报(理学版),2012,47(8):16~21,27.
[20]罗晓棠等.直觉模糊完全正则子半群及其同态[J].模糊系统与数学,2013,27(6):52~58.
[21]裴峥.格蕴涵代数中的直觉模糊滤子[J].西华大学学报(自然科学版),2007,26(2):17~20.
[22]许伟涛,徐扬,潘小东.格蕴涵代数中的直觉模糊关联滤子[J].江南大学学报(自然科学版),2009,8(6):736~739.
[23]朱华,赵建彬,徐扬.格蕴涵代数中的直觉模糊理想[J].模糊系统与数学,2014,28(1):23~27.