Vol.3 No.04(2014), Article ID:14177,4 pages
DOI:10.12677/AAM.2014.34023

Generalization of Deng’s Pseudo-Metric on the Lattices

Peng Chen1,2*, Feifei Guo1

1Mathematics and Statistics Institute, Henan University of Science and Technology, Luoyang

2College of Applied Science, Beijing University of Technology, Beijing

Email: *chenpengbeijing@sina.com

Received: Mar. 2nd, 2014; revised: Sep. 12th, 2014; accepted: Sep. 29th, 2014

ABSTRACT

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 to completely distributive lattice

Keywords:Deng’s Pseudo-Metric; Shi’s Pseudo-Metric, Fuzzy Point, Completely Distributive Lattice

Deng式伪度量在格上的推广

1河南科技大学，数学与统计学院，洛阳

2北京工业大学，应用数理学院，北京

Email: *chenpengbeijing@sina.com

Deng伪度量，Shi伪度量，模糊点；完全分配格

1. 引言和预备

1) 如果，则

2)

3)

4)，这里使得

(N1)如果，那么

(N2)

(N3)

(N4)使得使得

(N4)*

2. 其它预备知识

3. 本文主要结果

(M1) 如果，则

(M2)

(M3);

(M4)，使得使得

.

(L1)如果，那么

(L2)

(L3)

(L4)使得使得

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

3. [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. [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. [5]   Wang, G.J. (1988) Theory of L-fuzzy topological space. Shanxi Normal University Publishers, Xian. (In Chinese).

6. [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. [7]   Shi, F.G. (2001) Pointwise pseudo-metrics in L-fuzzy set theory. Fuzzy Sets and Systems, 121, 200-216.

8. [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.

NOTES

*通讯作者。