ET-lipschitzian and ET-kernel aggregation operators

Authors:
J. Jacas;J. Recasens
Affiliations:
Sec Matemàtiques i Informàtica, ETS Arquitecura de Barcelona, Universitat Politècnica de Catalunya, Diagonal 649, 08028 Barcelona, Spain;Secció Matemàtiques i Informàtica, ETS Arquitectura del Vallès, Universitat Politècnica de Catalunya, Pere Serra 1-15, 08190 Sant Cugat del Vallès, Spain
Venue:
International Journal of Approximate Reasoning
Year:
2007

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Abstract

Lipschitzian and kernel aggregation operators with respect to natural T-indistinguishability operators E"T and their powers are studied. A t-norm T is proved to be E"T-lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T.