The Hausdorff fuzzy quasi-metric

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 2010 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 161, pages 1,078-1,096 (issn: 0165-0114,

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Authors: Jesús Rodríguez-López; Salvador Romaguera; José Manuel Sánchez-Álvarez;

doi: 10.1016/j.fss.2009.09.019

The Hausdorff fuzzy quasi-metric

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Abstract

Removing the condition of symmetry in the notion of a fuzzy (pseudo)metric, in Kramosil and Michalek's sense, one has the notion of a fuzzy quasi-(pseudo-)metric. Then for each fuzzy quasi-pseudo-metric on a set X we construct a fuzzy quasi-pseudo-metric on the collection of all nonempty subsets of X, called the Hausdorff fuzzy quasi-pseudo-metric. We investigate several properties of this structure and present several illustrative examples as well as an application to the domain of words. The notion of Hausdorff fuzzy quasi-pseudo-metric when quasi-pseudo-metric fuzziness is considered in the sense of George and Veeramani is also discussed.

Supported by the Plan Nacional I+D+i and FEDER, under Grant MTM2006-14925-C02-01.

Related Organizations

Universitat Politècnica de València
Spain

Keywords

Fuzzy topology, Hausdorff fuzzy quasi-pseudo-metric, The domain of words, Precompact, preorder, Complete, complete, Preorder, Metric spaces, metrizability, MATEMATICA APLICADA, Theory of fuzzy sets, etc., precompact, domain of words, The Hausdorff fuzzy quasi-pseudo-metric

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