Scalar cardinalities of finite fuzzy sets for t-norms and t-conorms

Authors:
J. Casasnovas;J. Torrens
Affiliations:
Department of Mathematics and Computer Science, University of Balearic Islands, Crta. de Valldemossa, Km. 7.5, 07071 Palma de Mallorca, Spain;Department of Mathematics and Computer Science, University of Balearic Islands, Crta. de Valldemossa, Km. 7.5, 07071 Palma de Mallorca, Spain
Venue:
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Year:
2003

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Abstract

An axiomatic approach to scalar cardinalities of finite fuzzy sets involving t-norms and t-conorms is presented. A characterization theorem for these cardinalities is proved and it is also proved that some standard properties remain true. On the other hand, properties like finite additivity, valuation property or finite subadditivity depend on the t-norm and the t-conorm.