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点式p.度量的等价公理及其应用 被引量：1

Equivalent Axioms of Pointwise p. Metric and Its Applications
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摘要 给出了点式p.度量在L格上的一组等价公理,通过定义O-nbd映射簇对它进行了刻画,同时还给出了它的一些其它性质及其它在L-实直线上的应用。 In this paper, it is pointed out that the axioms of pointwise p. metric can be replaced by another a set of axioms and based on this, pointwise p. metric is depicted by O-nbd mapping set defined and some other propertises are presented. Moreover, some results by its applications to the L-real line are showed.
作者 陈鹏
机构地区 西部矿业股份有限公司
出处 《模糊系统与数学》 CSCD 北大核心 2009年第1期59-65,共7页 Fuzzy Systems and Mathematics
关键词 L-拓扑 点式P.度量 O-nbd映射簇 L-实直线 L-topology Pointwise p. Metric O-nbd Mapping Set L-real Line
分类号 O189 [理学—基础数学]
  • 相关文献

参考文献13

  • 1Chen P. Equivalent form of pointwise p. metric and its some properties[J]. Fuzzy Systems and Mathematics,2006, 20 (Supplement) : 17-20.
  • 2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
  • 3Chen 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.
  • 4Erceg M A. Metric spaces in fuzzy set theory[J].Math. Anal. Appl. , 1979,69:205-230.
  • 5Gierz G, et al. A compendium of continuous lattices[M]. New York:Springer-Verlag,1980.
  • 6Hutton B. Uniformities on fuzzy topological spaces[J]. Math. Anal. Appl. , 1977,58 : 559- 571.
  • 7Pu 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.
  • 8Peng Y W. Simplification of Ereeg's fuzzy metric function and its application[J]. Fuzzy Sets and Systems,1993,54: 181-189.
  • 9Shi F G. Pointwise quasi-uniformities and p.q. metrics on completely distributive lattices[J]. Acta Math. Sinica, 1996,39(5) :701-706.
  • 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2

共引文献10

同被引文献10

  • 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
  • 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.
  • 8Peng Y W. Simplification of Erceg's fuzzy metric function and its application[J3. Fuzzy Sets and Systems, 1993,54: 181-189.
  • 9Shi F G. Pointwise pseudo-metrics in L-fuzzy set theory[J]. Fuzzy Sets and Systems,2001,121:200-216.
  • 10Wang G J. Theory of L-fuzzy topological space EM']. Xi-an: Shannxi Normal University Publishers, 1988 (in Chinese).

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模糊系统与数学
2009年 第1期

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