格蕴涵代数(∈,∈∨_(q(λ,μ)))-模糊子代数
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摘要
本文从以下几个方面对格蕴涵代数的(∈,∈∨q(λ,μ))-模糊子代数进行了详细的研究。首先给出了点态化的(∈,∈∨q(λ,μ))-模糊子代数和广义模糊子代数的概念,讨论了两者之间的等价关系;其次给出了(∈,∈∨q(λ,μ))-模糊子代数的一些等价刻画,并研究了其相关性质;再次讨论了(∈,∈∨q(λ,μ))-模糊子代数的同态像与同态原像的基本性质;最后还研究了(∈,∈∨q(λ,μ))-模糊子代数的直积。
In this paper,we carry out a detailed investigation into the(∈,∈∨q(λ,μ))-fuzzy subalgebra of the lattice implication algebra from the following aspects.Firstly,the concepts of the pointwise(∈,∈∨q(λ,μ))-fuzzy subalgebra and generalized fuzzy subalgebra are introduced,and the relationship between them is also discussed.Secondly,we present some equivalent descriptions of the(∈,∈∨q(λ,μ))-fuzzy subalgebra and discusses the related properties;Thirdly,we discuss some basic properties of homomorphic image and homomorphic preimage of the(∈,∈∨q(λ,μ))-fuzzy subalgebra.Finally,the direct product of the(∈,∈∨q(λ,μ))-fuzzy subalgebra is studied.
In this paper,we carry out a detailed investigation into the(∈,∈∨q(λ,μ))-fuzzy subalgebra of the lattice implication algebra from the following aspects.Firstly,the concepts of the pointwise(∈,∈∨q(λ,μ))-fuzzy subalgebra and generalized fuzzy subalgebra are introduced,and the relationship between them is also discussed.Secondly,we present some equivalent descriptions of the(∈,∈∨q(λ,μ))-fuzzy subalgebra and discusses the related properties;Thirdly,we discuss some basic properties of homomorphic image and homomorphic preimage of the(∈,∈∨q(λ,μ))-fuzzy subalgebra.Finally,the direct product of the(∈,∈∨q(λ,μ))-fuzzy subalgebra is studied.
引文
[1]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8:338~353.
[2]Rosenfeld A.Fuzzy groups[J].Journal of Mathematical Analysis and Applications,1971,35:512~517.
[3]Zadeh L A.The concepts of a linguistic variable and itsapplication to approximate reasoning(I)(II)(III)[J].Information Sciences,1975,(8):199;1975,(8):301;1975,(9):43.
[4]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,1980,76:571~599.
[5]Pu P M,Liu Y M.Fuzzy Topology(II):Product and quotient spaces[J].Journal Of Mathematical Analysis And Applications,1980,77:20~37.
[6]Bhakat S K,Das P.On the definition of a fuzzy subgroup[J].Fuzzy Sets Systems,1992,51:235~241.
[7]Bhakat S K,Das P.Fuzzy subgroups[J].Fuzzy Sets Systems,1996,80:359~368.
[8]Bhakat S K,Das P.Fuzzy subrings and ideals redefined[J].Fuzzy Sets Systems,1996,81:383~393.
[9]Liao Z H,Gu H.Fuzzy normal subgroup[J].Fuzzy Systems and Mathematics,2006,20(5):38~43.
[10]Chen M,Liao Z H.fuzzy subsemigroups and fuzzy ideals of semigroups[C]//The Sixth International Conference on Information and Management Sciences.California Polytechnic State Univesity press,2007:575~579.
[11]Du J,Liao Z H.Generalized fuzzy ideal of algebra[C]//The Fourth International Conference on Fuzzy Systems and Knowledge Discovery.IEEE Press,2007:294~299.
[12]Zhou J,Liao Z H.Generalized(α,β)-convex fuzzy cones[C]//The 2008IEEE International Conference on Fuzzy Systems.IEEE Press,2008:439~442.
[13]Liao Z H,Hu M H,Chen M,Yi L H,Rui M l,Lu J H,Liu C Z.Generalized fuzzy interior ideals in semigroups[C]//2010Third International Joint Conference on Computational Science and Optimization.IEEE Press,2010:197~200.
[14]易丽华,廖祖华.半群的(∈,∈∨q(λ,μ))-模糊n伪理想与Drazin半群的刻画[J].模糊系统与数学,2009,23(5):48~55.
[15]廖祖华,陈敏.(∈,∈∨q(λ,μ))-模糊子近环和理想[J].模糊系统与数学,2009,23(6):12~16.
[16]胡淼菡,廖祖华,易丽华,芮明力.半环的(∈,∈∨q(λ,μ))-模糊双理想[J].模糊系统与数学,2011,25(5):69~76.
[17]刘春芝,廖祖华,曹姝,胡淼菡,芮明力.(∈,∈∨q(λ,μ))-模糊子格[J].模糊系统与数学,2011,25(5):54~59.
[18]芮明力,廖祖华,胡淼菡,陆金花.广义模糊子坡与(∈,∈∨q(λ,μ))-模糊子坡[J].模糊系统与数学,2011,25(6):60~68.
[19]Liao Z H,Yi L H,Hu M H.(∈,∈∨q(λ,μ))-fuzzy k-ideals of semigroups[J].Journal of Mathematics,2012,32(2):191~205.
[20]廖祖华,胡淼菡,芮明力,曹姝.链式条件下的半环的(∈,∈∨q(λ,μ))-模糊双理想[J].模糊系统与数学,2012,26(2):54~59.
[21]王德江,廖祖华,曹姝,宋璐瑶,刘春芝.R-广义模糊子格[J].山东大学学报(理学版),2012,47(1):93~97.
[22]吴望名.Fuzzy蕴涵代数[J].模糊系统与数学,1990,4(1):56~64.
[23]徐扬.格蕴涵代数[J].西南交通大学学报,1993,(1):20~27.
[24]徐扬.模糊格蕴涵代数[J].西南交通大学学报,1995,30(2):121~127.
[25]Xu Y,Ruan D,Qin K Y,Liu J.Lattice-valued logic[M].Berlin:Springer,2003.
[26]刘熠,徐扬,秦亚.区间值(α,β)-模糊格蕴涵子代数[J].计算机科学,2011,38(4):263~266.
[27]秦学成,刘春辉.格蕴涵代数的区间值模糊子代数[J].纯粹数学与应用数学,2011,27(6):801~807.
[28]刘春辉.关于IV-模糊格蕴涵子代数[J].计算机工程与应用,2012,48(26):39~43.
[2]Rosenfeld A.Fuzzy groups[J].Journal of Mathematical Analysis and Applications,1971,35:512~517.
[3]Zadeh L A.The concepts of a linguistic variable and itsapplication to approximate reasoning(I)(II)(III)[J].Information Sciences,1975,(8):199;1975,(8):301;1975,(9):43.
[4]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,1980,76:571~599.
[5]Pu P M,Liu Y M.Fuzzy Topology(II):Product and quotient spaces[J].Journal Of Mathematical Analysis And Applications,1980,77:20~37.
[6]Bhakat S K,Das P.On the definition of a fuzzy subgroup[J].Fuzzy Sets Systems,1992,51:235~241.
[7]Bhakat S K,Das P.Fuzzy subgroups[J].Fuzzy Sets Systems,1996,80:359~368.
[8]Bhakat S K,Das P.Fuzzy subrings and ideals redefined[J].Fuzzy Sets Systems,1996,81:383~393.
[9]Liao Z H,Gu H.Fuzzy normal subgroup[J].Fuzzy Systems and Mathematics,2006,20(5):38~43.
[10]Chen M,Liao Z H.fuzzy subsemigroups and fuzzy ideals of semigroups[C]//The Sixth International Conference on Information and Management Sciences.California Polytechnic State Univesity press,2007:575~579.
[11]Du J,Liao Z H.Generalized fuzzy ideal of algebra[C]//The Fourth International Conference on Fuzzy Systems and Knowledge Discovery.IEEE Press,2007:294~299.
[12]Zhou J,Liao Z H.Generalized(α,β)-convex fuzzy cones[C]//The 2008IEEE International Conference on Fuzzy Systems.IEEE Press,2008:439~442.
[13]Liao Z H,Hu M H,Chen M,Yi L H,Rui M l,Lu J H,Liu C Z.Generalized fuzzy interior ideals in semigroups[C]//2010Third International Joint Conference on Computational Science and Optimization.IEEE Press,2010:197~200.
[14]易丽华,廖祖华.半群的(∈,∈∨q(λ,μ))-模糊n伪理想与Drazin半群的刻画[J].模糊系统与数学,2009,23(5):48~55.
[15]廖祖华,陈敏.(∈,∈∨q(λ,μ))-模糊子近环和理想[J].模糊系统与数学,2009,23(6):12~16.
[16]胡淼菡,廖祖华,易丽华,芮明力.半环的(∈,∈∨q(λ,μ))-模糊双理想[J].模糊系统与数学,2011,25(5):69~76.
[17]刘春芝,廖祖华,曹姝,胡淼菡,芮明力.(∈,∈∨q(λ,μ))-模糊子格[J].模糊系统与数学,2011,25(5):54~59.
[18]芮明力,廖祖华,胡淼菡,陆金花.广义模糊子坡与(∈,∈∨q(λ,μ))-模糊子坡[J].模糊系统与数学,2011,25(6):60~68.
[19]Liao Z H,Yi L H,Hu M H.(∈,∈∨q(λ,μ))-fuzzy k-ideals of semigroups[J].Journal of Mathematics,2012,32(2):191~205.
[20]廖祖华,胡淼菡,芮明力,曹姝.链式条件下的半环的(∈,∈∨q(λ,μ))-模糊双理想[J].模糊系统与数学,2012,26(2):54~59.
[21]王德江,廖祖华,曹姝,宋璐瑶,刘春芝.R-广义模糊子格[J].山东大学学报(理学版),2012,47(1):93~97.
[22]吴望名.Fuzzy蕴涵代数[J].模糊系统与数学,1990,4(1):56~64.
[23]徐扬.格蕴涵代数[J].西南交通大学学报,1993,(1):20~27.
[24]徐扬.模糊格蕴涵代数[J].西南交通大学学报,1995,30(2):121~127.
[25]Xu Y,Ruan D,Qin K Y,Liu J.Lattice-valued logic[M].Berlin:Springer,2003.
[26]刘熠,徐扬,秦亚.区间值(α,β)-模糊格蕴涵子代数[J].计算机科学,2011,38(4):263~266.
[27]秦学成,刘春辉.格蕴涵代数的区间值模糊子代数[J].纯粹数学与应用数学,2011,27(6):801~807.
[28]刘春辉.关于IV-模糊格蕴涵子代数[J].计算机工程与应用,2012,48(26):39~43.