Qualitative integrals and desintegrals --- towards a logical view

Authors:
Didier Dubois;Henri Prade;Agnès Rico
Affiliations:
IRIT, CNRS Université de Toulouse, France;IRIT, CNRS Université de Toulouse, France;ERIC, Université de Lyon, France
Venue:
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
Year:
2012

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Abstract

This paper presents several variants of Sugeno integral, and in particular the idea of (qualitative) desintegrals, a dual of integrals. When evaluating an item, desintegrals are maximal if no defects at all are present, while integrals are maximal if all advantages are sufficiently present. This idea leads to a bipolar representation of preferences, by means of a pair made of an integral and a desintegral, whose possibilistic logic counterparts are outlined (in the case where criteria are binary).