Deng式伪度量在格上的推广

doi:10.12677/AAM.2014.34023

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AAM >> Vol. 3 No. 4 (November 2014)

Deng式伪度量在格上的推广
Generalization of Deng’s Pseudo-Metric on the Lattices

全文下载: PDF(416KB) HTML PP.155-159 DOI: 10.12677/AAM.2014.34023
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作者:

陈鹏,郭飞飞：河南科技大学，数学与统计学院，洛阳

关键词:
Deng伪度量；Shi伪度量；模糊点；L^x完全分配格；Deng’s Pseudo-Metric; Shi’s Pseudo-Metric； Fuzzy Point；L^x Completely Distributive Lattice

摘要:

本文研究了Deng式伪度量的一些性质，并给出了它的一种等价形式，由此把定义在I^x上的Deng式伪度量推广到完全分配格L^x上。

In this paper, we research some properties of Deng’s pseudo-metric, and show an equivalent form of its axioms. Therefore, we generalize Deng’s pseudo-metric from I^x to completely distributive lattice L^x。

文章引用:
陈鹏, 郭飞飞. Deng式伪度量在格上的推广[J]. 应用数学进展, 2014, 3(4): 155-159. http://dx.doi.org/10.12677/AAM.2014.34023

参考文献

[1]	Erceg, M.A. (1979) Metric spaces in fuzzy set theory. Journal of Mathematical Analysis and Applications, 69, 205- 230.

[2]	Deng, Z.K. (1982) Fuzzy pseudo-metric spaces. Journal of Mathematical Analysis and Applications, 86, 74-79.

[3]	Pu, B.M. and Liu, Y.M. (1980) Fuzzy Topology I, neighborhood structure of a fuzzy point and Moore-Smith Convergence. Journal of Mathematical Analysis and Applications, 76, 571-599.

[4]	王国俊 (1982) 领域方法在Fuzzy拓扑学中的困难. 模糊数学, 1, 113-116.

[5]	Wang, G.J. (1988) Theory of L-fuzzy topological space. Shanxi Normal University Publishers, Xian. (In Chinese).

[6]	陈鹏 (2008) L-拓扑中几种度量的性质及其关系. 博士论文, 北京理工大学, 北京.

[7]	Shi, F.G. (2001) Pointwise pseudo-metrics in L-fuzzy set theory. Fuzzy Sets and Systems, 121, 200-216.

[8]	梁基华 (1984) 关于不分明度量空间的几个问题. 数学年刊, 1, 59-67.

[9]	陈鹏, 史富贵 (2007) Erceg度量的进一步简化及其性质. 数学进展, 5, 579-586.

AAM >> Vol. 3 No. 4 (November 2014)

Deng式伪度量在格上的推广Generalization of Deng’s Pseudo-Metric on the Lattices

Deng式伪度量在格上的推广
Generalization of Deng’s Pseudo-Metric on the Lattices