模糊Domain上的模糊序同态及其性质
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摘要
通过引入模糊定向极小集和模糊Domain的基的概念,证明了模糊定向完备偏序集X是模糊Domain当且仅当X有基当且仅当x∈X,x有模糊定向极小集.基于模糊定向极小集和模糊Domain的基,研究了模糊Domain上的模糊序同态,证明了模糊Domain X的基到模糊Domain Y上的模糊序同态可以唯一扩张为模糊Domain X到模糊Domain Y上的模糊序同态.
By introducing the concepts of a fuzzy directed minimal set and a basis of fuzzy Domain, we prove that a fuzzy directed complete poset Xis a fuzzy Domain iff Xhas a basis iff for every element xof X,xhas the fuzzy directed minimal set.Based on the fuzzy directed minimal sets and the bases of fuzzy Domains,some properties of fuzzy order-homomorphisms of fuzzy Domains are investigated,and the fuzzy order-homomorphisms from the basis of Xinto a fuzzy Domain Ycould be uniquely extended to the fuzzy order-homomorphisms from Xinto Y.
By introducing the concepts of a fuzzy directed minimal set and a basis of fuzzy Domain, we prove that a fuzzy directed complete poset Xis a fuzzy Domain iff Xhas a basis iff for every element xof X,xhas the fuzzy directed minimal set.Based on the fuzzy directed minimal sets and the bases of fuzzy Domains,some properties of fuzzy order-homomorphisms of fuzzy Domains are investigated,and the fuzzy order-homomorphisms from the basis of Xinto a fuzzy Domain Ycould be uniquely extended to the fuzzy order-homomorphisms from Xinto Y.
引文
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[2]Yang Zhongqiang.A cartesian closed subcategory of CONT which contains all continuous domains[J].Information Sciences,2004,168:1-7.
[3]覃锋.连续格的序同态[J].江西师范大学学报:自然科学版,2000,24(2):126-129.
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[5]Zhang Qiye,Fan Lei.Continuity in quantitative domains[J].Fuzzy Sets and Systems,2005,154:118-131.
[6]姚卫.模糊偏序集上的模糊Scott拓扑及模糊拓扑空间的特殊化L-序[D].北京:北京理工大学数学学院,2008.
[7]Wang Kaiyun,Zhao Bin.Fuzzy domains and a classification theorem[C]∥Wang Guojun,Zhao Bin,Li Yongming.Proceedings of the 3rd International Conference on Quantitative Logic and Soft Computing.New Jersey:World Scientific Publishing,2012:512-519.
[8]刘敏,赵彬.FZ-Domain的基与抽象基的RZ-理想完备化[J].陕西师范大学学报:自然科学版,2011,39(2):8-12.
[9]Gierz G,Hofmann K H,Keimel K,et al.Continuous lattices and Domains[M].Cambridge:Cambridge University Press,2003:48-176.
[10]Wagner K R.Liminf convergence inΩ-categories[J].Theoretical Computer Science,1997,184:61-104.
[11]Bělohlávek R.Fuzzy relational systems:foundations and principles[M].New York:Kluwer Academic Publishers,Plenum Publishers,2002:203-271.
[12]Bělohlávek R.Concept lattices and order in fuzzy logic[J].Annals of Pure and Applied Logic,2004,128:277-298.
[13]Yao Wei.Quantative domains via fuzzy sets:partⅠ:Continuity of fuzzy directed complete posets[J].Fuzzy Sets and Systems,2010,161(7):983-987.
[14]Lai Hongliang,Zhang Dexue.Complete and directed completeΩ-categories[J].Theoretical Computer Science,2007,388:1-25.
[15]姚卫.模糊Domain中范畴间的同构与等价[R].西安:陕西师范大学数学与信息科学学院,2012.
[2]Yang Zhongqiang.A cartesian closed subcategory of CONT which contains all continuous domains[J].Information Sciences,2004,168:1-7.
[3]覃锋.连续格的序同态[J].江西师范大学学报:自然科学版,2000,24(2):126-129.
[4]Fan Lei.A new approach to quantitative domain theory[J].Electronic Notes in Theoretical Computer Science,2001,45:77-87.
[5]Zhang Qiye,Fan Lei.Continuity in quantitative domains[J].Fuzzy Sets and Systems,2005,154:118-131.
[6]姚卫.模糊偏序集上的模糊Scott拓扑及模糊拓扑空间的特殊化L-序[D].北京:北京理工大学数学学院,2008.
[7]Wang Kaiyun,Zhao Bin.Fuzzy domains and a classification theorem[C]∥Wang Guojun,Zhao Bin,Li Yongming.Proceedings of the 3rd International Conference on Quantitative Logic and Soft Computing.New Jersey:World Scientific Publishing,2012:512-519.
[8]刘敏,赵彬.FZ-Domain的基与抽象基的RZ-理想完备化[J].陕西师范大学学报:自然科学版,2011,39(2):8-12.
[9]Gierz G,Hofmann K H,Keimel K,et al.Continuous lattices and Domains[M].Cambridge:Cambridge University Press,2003:48-176.
[10]Wagner K R.Liminf convergence inΩ-categories[J].Theoretical Computer Science,1997,184:61-104.
[11]Bělohlávek R.Fuzzy relational systems:foundations and principles[M].New York:Kluwer Academic Publishers,Plenum Publishers,2002:203-271.
[12]Bělohlávek R.Concept lattices and order in fuzzy logic[J].Annals of Pure and Applied Logic,2004,128:277-298.
[13]Yao Wei.Quantative domains via fuzzy sets:partⅠ:Continuity of fuzzy directed complete posets[J].Fuzzy Sets and Systems,2010,161(7):983-987.
[14]Lai Hongliang,Zhang Dexue.Complete and directed completeΩ-categories[J].Theoretical Computer Science,2007,388:1-25.
[15]姚卫.模糊Domain中范畴间的同构与等价[R].西安:陕西师范大学数学与信息科学学院,2012.