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Axiomatisation of discrete fuzzy integrals with respect to possibility and necessity measures

Dubois, Didier and Rico, Agnès Axiomatisation of discrete fuzzy integrals with respect to possibility and necessity measures. (2016) In: 13th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2016), 19 September 2016 - 21 September 2016 (Sant Julia de Loria, Andorra).

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Official URL: http://dx.doi.org/10.1007/978-3-319-45656-0_8

Abstract

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.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Springer editor. This papers appears in Volume 9880 of Lecture Notes in Computer Science ISSN : 0302-9743 ISBN: 978-3-319-45655-3 The original PDF is available at: http://link.springer.com/chapter/10.1007%2F978-3-319-45656-0_8
HAL Id:hal-01445244
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Université Claude Bernard-Lyon I - UCBL (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:13 Jan 2017 10:11

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