Some complete metrics on spaces of fuzzy subsets

Authors:
Volker Krätschmer
Affiliations:
Statistik and Ökonometrie, Rechtsund Wirtschaftswissenschaftliche Fakultät, Universität des Saarlandes, Bau 31, Postfach 15 11 50, D-66041 Saarbrücken, Germany
Venue:
Fuzzy Sets and Systems - Fuzzy intervals
Year:
2002

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Abstract

The classes of the Lp,∞- and Lp-metrics play an important role to develop a probability theory in fuzzy sample spaces. All of these metrics are known to be separable, but not complete. The classes are closely related as for each Lp,∞-metric there exists some Lp-metric which induces the same topology. This paper deals with the completion of the Lp,∞- and Lp-metrics. We can also show that the relationship between the classes of Lp,∞- and Lp-metrics still holds for the obtained respective classes of their completions.