On the cardinalities of interval-valued fuzzy sets

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 2007 English Publisher:Elsevier BVJournal:Fuzzy Sets and Systems, volume 158, pages 1,728-1,750 (issn: 0165-0114,

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Authors: Glad Deschrijver; Pavol Král;

doi: 10.1016/j.fss.2007.01.005

On the cardinalities of interval-valued fuzzy sets

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Abstract

The paper deals with one of the possible extensions of axiomatic theory of scalar cardinalities of fuzzy sets with finite support. The extension is related to the interval-valued fuzzy sets. Their cardinality is introduced as a mapping to the set of closed subintervals of non-negative real numbers. Some of its properties are investigated and discussed with special regard to the valuation property, subadditivity property, complementarity rule, and the Cartesian product rule.

Related Organizations

Ghent University
Belgium
Matej Bel University
Slovakia

Keywords

scalar cardinality, intuitionistic fuzzy set, subadditivity, Cartesian product, Theory of fuzzy sets, etc., valuation, interval-valued fuzzy set, complementarity

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