模糊偏序集上的扩张定理
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摘要
借助于模糊Galois联络,在模糊偏序集上定义了完备扩张,并建立了模糊dcop和完备扩张之间的等价关系。此外,还定义了连续扩张,并得到模糊domain和连续扩张的等价刻画定理。
In this paper,based on fuzzy posets,we will introduce the concept of complete extension with the help of fuzzy Galois connection,and establish a characterization theorem between fuzzy dcpos and complete extension.Moreover,we also give the definition of continuous extension and obtain an equivalent characterization theorem of fuzzy domains by means of continuous extension.
In this paper,based on fuzzy posets,we will introduce the concept of complete extension with the help of fuzzy Galois connection,and establish a characterization theorem between fuzzy dcpos and complete extension.Moreover,we also give the definition of continuous extension and obtain an equivalent characterization theorem of fuzzy domains by means of continuous extension.
引文
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[2]Scott D S.Continuous lattices,topos,algebraic geometry and logic[C]//Lecture Notes in Mathematics.Berlin:Springer,1972,274:97~136.
[3]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8:338~353.
[4]Fan L.A new approach to quantitative domain theory[J].Electronic Notes in Theoretical Computer Science,2001,45:77~87.
[5]Zhang Q Y,Fan L.Continuity in quantitative domains[J].Fuzzy Sets and Systems,2005,154:118~131.
[6]Lai H L,Zhang D X.Complete and directed completeΩ-categories[J].Theoretical Computer Science,2007,388:1~12.
[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]Liu M,Zhao B.Two cartesian closed subcategories of fuzzy domains[J].Fuzzy Sets and Systems,2014,238:102~112.
[9]Wang K Y,Zhao B.Join-completions of L-ordered sets[J].Fuzzy Sets and Systems,2012,199:92~107.
[10]Goguen J A.L-fuzzy sets[J].Journal of Mathematical Analysis and Applications,1967,18:145~174.
[11]Belohlavek R.Lattice type fuzzy order and closure operators in fuzzy ordered sets[C]//Proceedings of the Joint Ninth IFSA World Congress and 20th NAFIPS International Conference.IEEE Press,Vancouver,Canada,2001:2281~2286.
[12]Belohlavek R.Fuzzy Galois connections[J].Mathematical Logic Quarterly,1999,45:497~504.
[13]Yao W,Lu L X.Fuzzy Galois connections on fuzzy posets[J].Mathematical Logic Quarterly,2009,55:84~91.
[14]Guo L K,Zhang G Q,Li Q G.Fuzzy closure systems on L-ordered sets[J].Mathematical Logic Quarterly,2011,57:281~291.
[15]Gierz G,et al.Continuous lattices and domains[M].Cambridge:Cambridge University Press,2003.