利用插入性质刻画模糊domain
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摘要
基于插入性质,结合某些特定的条件,给出了模糊domain的等价刻画。首先,在模糊dcpo中,定义了模糊定向逼近元,结合插入性质给出模糊domain的等价刻画;然后,利用模糊Scott拓扑,定义了它的模糊基,同样基于插入性质得到模糊domain的另外一个等价刻画。
Based on the interpolation property,some equivalent characterizations of the fuzzy domain are given under appropriate conditions.Firstly the notion of fuzzy direct approximation element is introduced in the fuzzy dcpo.Then,with the help of the interpolation property,equivalent characterizations of the fuzzy domain are obtained.Moreover,by defining the fuzzy base with respect to the fuzzy Scott topology,equivalent characterizations of the fuzzy domain are derived again via the interpolation property.
Based on the interpolation property,some equivalent characterizations of the fuzzy domain are given under appropriate conditions.Firstly the notion of fuzzy direct approximation element is introduced in the fuzzy dcpo.Then,with the help of the interpolation property,equivalent characterizations of the fuzzy domain are obtained.Moreover,by defining the fuzzy base with respect to the fuzzy Scott topology,equivalent characterizations of the fuzzy domain are derived again via the interpolation property.
引文
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[2] ZHANG Q Y,FAN L.Continuity in Quantitative Domains[J].Fuzzy Sets and Systems,2005,154:118-131.
[3] SMYTH M B.Quasi-Uniformities:Reconciling Domains with Metrie Spaces,Third Wordshop on Mathematical Foundations of Programming Language Semntics[J].Lecture Notes in Computer Scinence,1988,298:236-253.
[4] SUNDREHAUF P.Quasi-uniform Completeness in terms of Cauchy Nests[J].Acta Mathematica Hungarica,1995,69:47-54.
[5] FLAGG B,KOPERMAN R.Continuity Spaces:Reconciling Domains and Metric Spaces[J].Theoretical Computer Science,1997,177:111-138.
[6] WAGNER K R.Liminf Convergence in Categories[J].Theoretical Computer Science,1997,184:61-104.
[7] YAO W.Quantitative Domains via Fuzzy Sets:Part I:Continuity of Fuzzy Directed Complete Posets[J].Fuzzy Sets and Systems,2010,161:973-987.
[8] YAO W,SHI F G.Quantitative Domains via Fuzzy Sets:Part II:Fuzzy Scott Topology on Fuzzy Directed Complete Posets[J].Fuzzy Sets and Systems,2011,161:1-21.
[9]饶三平,李庆国.模糊Scott拓扑的T0性[J].南昌大学学报(理科版),2012,36(5):426-428.
[10] FAN L.A New Approach to Quantitative Domain Theory[J].Electronic Notes in Theoretical Computer Science,2001,45:77-87.
[11] LAI H L,ZHANG D X.Complete and Directed Complete categories[J].Theoretical Computer Science,2007,388:1-12.
[12] BIRKHOFF G.Lattice Theory[M].American Mathematical Society,Providence RI,1967.
[2] ZHANG Q Y,FAN L.Continuity in Quantitative Domains[J].Fuzzy Sets and Systems,2005,154:118-131.
[3] SMYTH M B.Quasi-Uniformities:Reconciling Domains with Metrie Spaces,Third Wordshop on Mathematical Foundations of Programming Language Semntics[J].Lecture Notes in Computer Scinence,1988,298:236-253.
[4] SUNDREHAUF P.Quasi-uniform Completeness in terms of Cauchy Nests[J].Acta Mathematica Hungarica,1995,69:47-54.
[5] FLAGG B,KOPERMAN R.Continuity Spaces:Reconciling Domains and Metric Spaces[J].Theoretical Computer Science,1997,177:111-138.
[6] WAGNER K R.Liminf Convergence in Categories[J].Theoretical Computer Science,1997,184:61-104.
[7] YAO W.Quantitative Domains via Fuzzy Sets:Part I:Continuity of Fuzzy Directed Complete Posets[J].Fuzzy Sets and Systems,2010,161:973-987.
[8] YAO W,SHI F G.Quantitative Domains via Fuzzy Sets:Part II:Fuzzy Scott Topology on Fuzzy Directed Complete Posets[J].Fuzzy Sets and Systems,2011,161:1-21.
[9]饶三平,李庆国.模糊Scott拓扑的T0性[J].南昌大学学报(理科版),2012,36(5):426-428.
[10] FAN L.A New Approach to Quantitative Domain Theory[J].Electronic Notes in Theoretical Computer Science,2001,45:77-87.
[11] LAI H L,ZHANG D X.Complete and Directed Complete categories[J].Theoretical Computer Science,2007,388:1-12.
[12] BIRKHOFF G.Lattice Theory[M].American Mathematical Society,Providence RI,1967.