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Deng伪度量与Erceg伪度量的关系 被引量：2

The Relation between Deng's Pseudo-metric and Erceg's Pseudo-metric
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摘要 证明一个Deng度量是一个Erceg度量,但反之不成立,并且证明Deng度量的拓扑可以被远域刻画且它所诱导的拓扑和m-一致结构就是Erceg度量所诱导的拓扑和Hutton一致结构。 In this paper, we point out that Deng＇s pseudo-metric is Erceg＇s pseudo-metric, but the converse is not true, prove that the topology induced by Deng＇ s pseudo-metric can characterized by Q-neighborhoods, therefore its topology is Q-C1, and what is more, show that Deng＇s topology and it＇s m-uniformity are respectively Erceg＇s topology and Hutton＇s uniformity.
作者 陈鹏
机构地区 河南科技大学数学与统计学院 北京工业大学应用数理学院
出处 《模糊系统与数学》 CSCD 北大核心 2015年第1期1-5,共5页 Fuzzy Systems and Mathematics
基金 河南科技大学博士启动项目(09001613) 河南科技大学科研创新能力培育基金资助项目(13000810)
关键词 Deng伪度量 Erceg伪度量 m-一致结构 Q-C1 Deng＇ s Pseudo-metric Erceg＇ s Pseudo-metric m-uniformity Q-C1
分类号 O189 [理学—基础数学]
  • 相关文献

参考文献11

  • 1陈鹏,史福贵.Erceg-度量的进一步简化及其性质[J].数学进展,2007,36(5):586-592. 被引量：11
  • 2陈鹏.点式p.度量的等价公理及其应用[J].模糊系统与数学,2009,23(1):59-65. 被引量：1
  • 3Chen P. The relation between two kinds of metrics on lattices[J]. Annals of Fuzzy Sets,Fuzzy Logic and Fuzzy Systems, 2011,1 (2) : 175- 181.
  • 4Deng Z K. Fuzzy pseudo-metric spaces[J]. J. Math. Anal. Appl. , 1982,86 : 74- 79.
  • 5Deng Z K. M-Uniformization and metrization of fuzzy topological spaces[J]. J. Math. Anal. Appl. , 1985,112 (2) :471 -486.
  • 6Erceg M A. Metric spaces in fuzzy set theory[J]. Math. Anal. Appl. , 1979,69:205-230.
  • 7Hutton B. Uniformities on fuzzy topological spaces[J]. J. Math. Anal. Appl. ,1977,58:559-571.
  • 8梁基华.关于不分明度量空间的几个问题.数学年刊：A辑,1984,6(1):59-67.
  • 9Peng Y W. Simplification of Erceg's fuzzy metric function and its application[J3. Fuzzy Sets and Systems, 1993,54: 181-189.
  • 10Shi F G. Pointwise pseudo-metrics in L-fuzzy set theory[J]. Fuzzy Sets and Systems,2001,121:200-216.

二级参考文献15

  • 1Chen P. Equivalent form of pointwise p. metric and its some properties[J]. Fuzzy Systems and Mathematics,2006, 20 (Supplement) : 17-20.
  • 2Chen P. Shi F G. A note on Erceg's pseudo-metricand pointwise pseudo-metric[J]. J. Mathematical Research and Exposition, 2008,28 (2):439- 443.
  • 3Erceg M A. Metric spaces in fuzzy set theory[J].Math. Anal. Appl. , 1979,69:205-230.
  • 4Gierz G, et al. A compendium of continuous lattices[M]. New York:Springer-Verlag,1980.
  • 5Hutton B. Uniformities on fuzzy topological spaces[J]. Math. Anal. Appl. , 1977,58 : 559- 571.
  • 6Pu B M, Liu Y M. Fuzzy Topology I. Neighborhood structure of a fuzzy point and Moore-Smith ConvergenceLJJ. Math. Anal. Appl. ,1980,76:571-599.
  • 7Peng Y W. Simplification of Ereeg's fuzzy metric function and its application[J]. Fuzzy Sets and Systems,1993,54: 181-189.
  • 8Shi F G. Pointwise quasi-uniformities and p.q. metrics on completely distributive lattices[J]. Acta Math. Sinica, 1996,39(5) :701-706.
  • 9Shi F G. Pointwise pseudo-metrics in L-fuzzy set theory[J]. Fuzzy Sets and Systems,2001,121:200-216.
  • 10Shi F G. Pointwise pseudo-metric on the L-real line[J]. Iranian Journal of Fuzzy Systems,2005,4:79- 88.

共引文献14

同被引文献22

  • 1梁基华.关于不分明度量空间的几个问题.数学年刊：A辑,1984,6(1):59-67.
  • 2王国俊.邻域方法在Fuzzy拓扑学中的困难.模糊数学,1982,4(2):113-116.
  • 3杨乐成.完全分配格上的p.q.度量理论[J].科学通报,1988,(4):247-250.
  • 4陈鹏,史福贵.Erceg-度量的进一步简化及其性质[J].数学进展,2007,36(5):586-592. 被引量：11
  • 5Chen P. The relation between two kinds of metrics on lattices[J]. Annals of Fuzzy Sets, Fuzzy Logic and Fuzzy Systems,2011,1(2):175-181.
  • 6Deng Z K. Fuzzy pseudo-metric spaces[J]. J. Math. Anal. Appl. ,1982,86:74-79.
  • 7Deng Z K. M-uniformization and metrization of fuzzy topological spaces[J]. J. Math. Anal. Appl. , 1985,112(2):471 -486.
  • 8Erceg M A. Metric spaces in fuzzy set theory[J]. Math. Anal. Appl. ,1979,69:205-230.
  • 9Gierz G, et al. A compendium of continuous lattices[M]. New York:Springer-Verlag, 1980.
  • 10Hutton B. Uniformities on fuzzy topological spaces[J]. J. Math. Anal. Appl. ,1977,58:559-571.

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二级引证文献1

模糊系统与数学
2015年 第1期

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