The authors introduce a family of extended pseudo-metrics for a class of fuzzy metric spaces. It enables to construct a metric on fuzzy metric spaces and the induced metric space shares many properties with the given fuzzy metric space. For example the same topology is generated and the spaces have the same completeness. The authors present some simple examples to illustrate possible applications of their results. However it is difficult to evaluate how these results contribute to the general theory of probabilistic metric spaces [\textit{B. Schweizer} and \textit{A. Sklar}, Probabilistic metric spaces. North Holland Series in Probability and Applied Mathematics. New York-Amsterdam-Oxford: North-Holland (1983; Zbl 0546.60010)].

Related Organizations

Chongqing University of Posts and Telecommunications
China (People's Republic of)
Chongqing University
China (People's Republic of)

Keywords

Isomorphic theory (including renorming) of Banach spaces, complete metric spaces, \(H\)-type \(t\)-norms, Fuzzy topology, Metric spaces, metrizability, fuzzy analysis, fuzzy metric, Theory of fuzzy sets, etc.

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average