%0 Conference Proceedings
%T Axiomatisation of discrete fuzzy integrals with respect to possibility and necessity measures
%+ Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA)
%+ Centre National de la Recherche Scientifique (CNRS)
%+ Entrepôts, Représentation et Ingénierie des Connaissances (ERIC)
%A Dubois, Didier
%A Rico, Agnés
%< avec comité de lecture
%( Modeling Decisions for Artificial Intelligence
%B 13th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2016)
%C Sant Julia de Loria, Andorra
%N 9880
%P pp. 94-105
%8 2016-09-19
%D 2016
%K Choquet integral
%K Sugeno integral
%K Possibility theory
%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]Conference papers
%X Necessity (resp. possibility) measures are very simple representations of epistemic uncertainty due to incomplete knowledge. In the present work, a characterization of discrete Choquet integrals with respect to a possibility or a necessity measure is proposed, understood as a criterion for decision under uncertainty. This kind of criterion has the merit of being very simple to define and compute. To get our characterization, it is shown that it is enough to respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the decision-maker preferences only reflect the plausibility ordering between states of nature. The obtained pessimistic (resp. optimistic) criterion is an average of the maximin (resp. maximax) criterion of Wald across cuts of a possibility distribution on the state space. The additional axiom can be also used in the axiomatic approach to Sugeno integral and generalized forms thereof. The possibility of axiomatising of these criteria for decision under uncertainty in the setting of preference relations among acts is also discussed.
%G English
%2 https://hal.science/hal-01445244/document
%2 https://hal.science/hal-01445244/file/dubois_17212.pdf
%L hal-01445244
%U https://hal.science/hal-01445244
%~ UNIV-TLSE2
%~ UNIV-TLSE3
%~ CNRS
%~ UNIV-LYON1
%~ UNIV-LYON2
%~ ERIC
%~ SMS
%~ UT1-CAPITOLE
%~ LYON2
%~ UDL
%~ UNIV-LYON
%~ IRIT
%~ IRIT-ADRIA
%~ IRIT-IA
%~ TOULOUSE-INP
%~ UNIV-UT3
%~ UT3-INP
%~ UT3-TOULOUSEINP