Fuzzy格上两种点式伪度量之间的关系
The Relation of Two Kinds of Pointed Pseudo-Metrics on Fuzzy Lattice

作者: 陈 鹏 :河南科技大学,数学与统计学院,洛阳;

关键词: Erceg伪度量点式伪度量Fuzzy格Erceg Pseudo-Metric A Pointwise Pseudo-Metric Fuzzy Lattice

摘要:
本文否定了文[1]的主要结果:一个点式Erceg伪度量是一个点式伪度量,并进一步给出相反的新的结论:一个点式伪度量是一个点式Erceg伪度量但反之不成立。

Abstract: In this paper, we negative the main result that an Erceg pseudo-metric is a pointwise pseudo-me- tric in [1], point out the wrong reasons in the process of its proof, and further put forward the new conclusion that a pointwise pseudo-metric is an Erceg pseudo-metric, but the converse is not true.

文章引用: 陈 鹏 (2014) Fuzzy格上两种点式伪度量之间的关系。 运筹与模糊学, 4, 47-51. doi: 10.12677/ORF.2014.44007

参考文献

[1] 梁基华 (2001) 关于Fuzzy格上点式伪度量的一个注记. 四川大学学报, 38, 455-498.

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

[3] Peng, Y.W. (1993) Simplification of Erceg’s fuzzy metric function and its application. Fuzzy Sets and Systems, 54, 181-189.

[4] Shi, F.G. (1996) Pointwise quasi-uniformities and p.q. metrics on completely distributive lattices. Acta Mathematics Sinica, 5, 701-706.

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

[6] 杨乐成 (1988) 完全分配格上的p.q.度量理论. 科学通报, 4, 247-250.

[7] Gierz, G., et al. (1980) A compendium of continuous lattices. Springer-Verlag, New York.

[8] Wang, G.J. (1988) Theory of $L$-fuzzy Topological Space. Shanxi Normal University Publishers, Xian.

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