模糊Z-Quantale范畴的反射子范畴
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摘要
利用模糊Quantale上的模糊预核映射,证明模糊Quantale范畴是模糊Z-Quantale范畴的反射子范畴,给出由万有映射像集生成的模糊Quantale的具体结构,并讨论由反射子构造的模糊Galois伴随.
By using the notion of fuzzy pre-nuclei mapping on fuzzy Quantale,we proved that the category of fuzzy Quantale was a reflective subcategory of the category of fuzzy Z-Quantale,gave the concrete structure of the fuzzy Quantale generated by the image set of universal mapping,and discussed the fuzzy Galois connection constructed by the reflector.
By using the notion of fuzzy pre-nuclei mapping on fuzzy Quantale,we proved that the category of fuzzy Quantale was a reflective subcategory of the category of fuzzy Z-Quantale,gave the concrete structure of the fuzzy Quantale generated by the image set of universal mapping,and discussed the fuzzy Galois connection constructed by the reflector.
引文
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[11]FAN Lei.A New Approach to Quantitative Domain Theory[J].Electronic Notes in Theoretical Computer Science,2001,45(1):77-87.
[12]Belohlvek R.Fuzzy Relational Systems:Foundations and Principles[M].New York:Springer,2002.
[13]Goguen J A.L-Fuzzy Sets[J].Journal of Mathematical Analysis and Applications,1967,18(1):145-174.
[14]ZHANG Qiye,FAN Lei.Continuity in Quantitative Domains[J].Fuzzy Sets and Systems,2005,154(1):118-131.
[15]ZHANG Qiye,XIE Weixian,FAN Lei.Fuzzy Complete Lattices[J].Fuzzy Sets and Systems,2009,160(16):2275-2291.
[16]Rodabaugh S E.Powerset Operator Foundations for Poslat Fuzzy Set Theories and Topologies[M]//H9hle U,Rodabaugh S E.Mathematics of Fuzzy Sets:Logic,Topology,and Measure Theory.New York:Springer,1999:91-116.
[17]LU Jing,WANG Kaiyun,ZHAO Bin.K-Flat Projective Fuzzy Quantales[J].Iranian Journal of Fuzzy Systems,2017,14(5):65-81.
[18]Kelly M.Basic Concepts of Enriched Category Theory[M].Cambridge:Cambridge University Press,1982.
[19]YAO Wei,LU Lingxia.Fuzzy Galois Connections on Fuzzy Posets[J].Mathematical Logic Quarterly,2009,55(1):105-112.
[2]Mulvey C J,Pelletier J W.On the Quantisation of Points[J].Journal of Pure and Applied Algebra,2001,159(2/3):231-295.
[3]汪开云,赵彬.Z-Quantale及其范畴性质[J].数学学报(中文版),2010,53(5):997-1006.(WANG Kaiyun,ZHAO Bin.Z-Quantales and Their Categorical Properties[J].Acta Mathematica Sinica(Chinese Series),2010,53(5):997-1006.)
[4]鲁静,汪开云,赵彬.Z-Quantale的进一步结果[J].数学学报(中文版),2015,58(6):911-922.(LU Jing,WANG Kaiyun,ZHAO Bin.Some Further Results on Z-Quantales[J].Acta Mathematica Sinica(Chinese Series),2015,58(6):911-922.)
[5]Zadeh L A.Fuzzy Sets[J].Information&Control,1965,8(3):338-353.
[6]汪开云.模糊Domain与模糊Quantale中若干问题的研究[D].西安:陕西师范大学,2012.(WANG Kaiyun.Some Researches on Fuzzy Domains and Fuzzy Quantales[D].Xi'an:Shaanxi Normal University,2012.)
[7]董倩.Quantale的左半可换商及模糊Z-Quantale结构[D].西安:陕西师范大学,2016.(DONG Qian.The Largest Left Semi-commutative Quotient of a Quantale and the Fuzzification of Z-Quantale Structures[D].Xi'an:Shaanxi Normal University,2016.)
[8]Admek J,Herrlich H,Strecker G E.Abstract and Concrete Categories.The Joy of Cats[M].New York:John Wiley&Sons,Inc,1990.
[9]Rosenthal K I.Quantales and Their Applications[M].New York:Longman Scientific and Technical,1990.
[10]Lawvere F W.Metric Spaces,Generalized Logic,and Closed Categories[J].Rendiconti del Seminario Matématico e Fisico di Milano,1973,43(1):135-166.
[11]FAN Lei.A New Approach to Quantitative Domain Theory[J].Electronic Notes in Theoretical Computer Science,2001,45(1):77-87.
[12]Belohlvek R.Fuzzy Relational Systems:Foundations and Principles[M].New York:Springer,2002.
[13]Goguen J A.L-Fuzzy Sets[J].Journal of Mathematical Analysis and Applications,1967,18(1):145-174.
[14]ZHANG Qiye,FAN Lei.Continuity in Quantitative Domains[J].Fuzzy Sets and Systems,2005,154(1):118-131.
[15]ZHANG Qiye,XIE Weixian,FAN Lei.Fuzzy Complete Lattices[J].Fuzzy Sets and Systems,2009,160(16):2275-2291.
[16]Rodabaugh S E.Powerset Operator Foundations for Poslat Fuzzy Set Theories and Topologies[M]//H9hle U,Rodabaugh S E.Mathematics of Fuzzy Sets:Logic,Topology,and Measure Theory.New York:Springer,1999:91-116.
[17]LU Jing,WANG Kaiyun,ZHAO Bin.K-Flat Projective Fuzzy Quantales[J].Iranian Journal of Fuzzy Systems,2017,14(5):65-81.
[18]Kelly M.Basic Concepts of Enriched Category Theory[M].Cambridge:Cambridge University Press,1982.
[19]YAO Wei,LU Lingxia.Fuzzy Galois Connections on Fuzzy Posets[J].Mathematical Logic Quarterly,2009,55(1):105-112.