%0 Journal Article
%T Residuated variants of Sugeno integrals: Towards new weighting schemes for qualitative aggregation methods
%+ Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA)
%+ Centre National de la Recherche Scientifique (CNRS)
%+ Equipe de Recherche en Ingénierie des Connaissances (ERIC)
%A Dubois, Didier
%A Prade, Henri
%A Rico, Agnés
%< avec comité de lecture
%@ 0020-0255
%J Information Sciences
%I Elsevier
%V vol. 329
%P pp. 765-781
%8 2016-09
%D 2016
%R 10.1016/j.ins.2015.09.034
%K Sugeno integral
%K Gödel implication
%K Possibility theory
%K Bipolarity
%K Multicriteria evaluation
%Z Computer Science [cs]/Artificial Intelligence [cs.AI]
%Z Computer Science [cs]/Machine Learning [cs.LG]
%Z Computer Science [cs]/Logic in Computer Science [cs.LO]
%Z Computer Science [cs]/Computation and Language [cs.CL]Journal articles
%X Sugeno integrals and their particular cases such as weighted minimum and maximum have been used in multiple-criteria aggregation when the evaluation scale is qualitative. This paper proposes two new variants of weighted minimum and maximum, where the criteria weights play the role of tolerance thresholds. These variants require the use of a residuated structure, equipped with an involutive negation. We propose residuated counterparts of Sugeno integrals, where the weights bear on subsets of criteria, and we study their properties, showing they are analogous to Sugeno integrals to a large extent. Finally we propose dual aggregation operations, we call desintegrals, where an item is evaluated in terms of its defects rather than in terms of its positive features. Desintegrals are maximal when no defects at all are present, while integrals are maximal when all merits are sufficiently present. Qualitative integrals and desintegrals suggest a possible approach to bipolar evaluation processes where items are judged both in terms of merits and defects that are not independent of one another.
%G English
%2 https://hal.science/hal-01538305/document
%2 https://hal.science/hal-01538305/file/dubois_16901.pdf
%L hal-01538305
%U https://hal.science/hal-01538305
%~ UNIV-TLSE2
%~ UNIV-TLSE3
%~ CNRS
%~ UNIV-LYON2
%~ ERIC
%~ SMS
%~ UT1-CAPITOLE
%~ LYON2
%~ UDL
%~ IRIT
%~ IRIT-ADRIA
%~ IRIT-IA
%~ TOULOUSE-INP
%~ UNIV-UT3
%~ UT3-INP
%~ UT3-TOULOUSEINP