Deng式伪度量在格上的推广
Generalization of Deng’s Pseudo-Metric on the Lattices
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Ix上的Deng式伪度量推广到完全分配格Lx上。
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 Ix to completely distributive lattice Lx。
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.
|