模糊Z_L-紧完备偏序集及扩张定理
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摘要
本文引入了模糊Z_L-紧完备偏序集,模糊Z_L-紧偏序集和模糊Z_L-闭支撑的概念,给出了模糊Z_L-完备偏序集的等价刻画。在此基础上研究了模糊Z_L-紧集的扩张定理以及扩张映射的性质。
This paper introduces the concepts of fuzzy Z_L-core complete poset, fuzzy Z_L-core poset and fuzzy Z_L-closed support. Then we study the equivalent characterization of fuzzy Z_L complete poset. Based on these, we show the extension theorem of fuzzy Z_L-compact sets and the property of the extension map.
This paper introduces the concepts of fuzzy Z_L-core complete poset, fuzzy Z_L-core poset and fuzzy Z_L-closed support. Then we study the equivalent characterization of fuzzy Z_L complete poset. Based on these, we show the extension theorem of fuzzy Z_L-compact sets and the property of the extension map.
引文
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[14]饶三平.模糊Domain的基理论研究及其推广[D].长沙:湖南大学,2014.
[15]Ma N,Zhao B.Some results on fuzzy ZL-continuous(algebraic)Poset[J].Soft Computing,2018,22:4549~4559.
[16]Belohlavek R.Fuzzy relational systems,foundations and principles[M].New York:Kluwer Academic Publishers,Plenum Publishers,2002.
[17]Belohlavek R.Some properties of residuated lattices[J].Czechoslovak Mathematical Journal,2004,54:161~171.
[2]Wright B,Wagner E G,Thather J W.A uniform approach to inductive posets and inductive closure[J].Theoretical Computer Science,1978,1:57~77.
[3]Bandelt J,Erne M.The category of Z-continuous posets[J].Journal of Pure and Applied Algebra,1983,30:219~226.
[4]Baranga A.Z-continuous posets[J].Discrete Mathematics,1996,152:33~45.
[5]Erne M.Z-continuous posets and their topological manifestation[J].Applied Categirical Structure,1999,7:31~70.
[6]Erne M,Zhao S.Z-join spectra of Z-supercompactly generated lattices[J].Applied Categirical Structure,2001,9:41~63.
[7]Fan L.A new approach to quantitative domain theory[J].Theoretical Computer Science,2001,45:77~87.
[8]Zhang Y,Xie W X,Fan L.Fuzzy complete lattices[J].Fuzzy Sets and Systems,2009,160:2275~2291.
[9]Xie X,Zhang Q Y,Fan L.The Dedekind-Mac Nillee completions for fuzzy posets[J].Fuzzy Sets and Systems,2009,160:2292~2316.
[10]Yao W.Quantitative domains via fuzzy sets:Part I:Continuity of fuzzy directed complete posets[J].Fuzzy Sets and Systems,2010,161:973~987.
[11]Yao W.Quantitative domains via fuzzy sets:Part II:Fuzzy Scott topology on fuzzy directed-complete posets[J].Fuzzy Sets and Systems,2011,173:60~80.
[12]Liu M,Zhao B.Two cartesian closed subcategories of fuzzy domains[J].Fuzzy sets and systems,2014,238:102~112.
[13]赵娜娜.模糊Z-Domain及其相关范畴性质[D].西安:陕西师范大学,2011.
[14]饶三平.模糊Domain的基理论研究及其推广[D].长沙:湖南大学,2014.
[15]Ma N,Zhao B.Some results on fuzzy ZL-continuous(algebraic)Poset[J].Soft Computing,2018,22:4549~4559.
[16]Belohlavek R.Fuzzy relational systems,foundations and principles[M].New York:Kluwer Academic Publishers,Plenum Publishers,2002.
[17]Belohlavek R.Some properties of residuated lattices[J].Czechoslovak Mathematical Journal,2004,54:161~171.