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New axiomatisations of discrete quantitative and qualitative possibilistic integrals

Dubois, Didier and Rico, Agnès New axiomatisations of discrete quantitative and qualitative possibilistic integrals. (2018) Fuzzy Sets and Systems, 343. 3-19. ISSN 0165-0114

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Official URL: https://doi.org/10.1016/j.fss.2017.06.007

Abstract

Necessity (resp. possibility) measures are very simple min-decomposable (resp. max-decomposable) representations of epistemic uncertainty due to incomplete knowledge. They can be used in both quantitative and qualitative settings. In the present work, we revisit Choquet and Sugeno integrals as criteria for decision under uncertainty and propose new axioms when uncertainty is representable in possibility theory. First, a characterization of Choquet integral with respect to a possibility or a necessity measure is proposed. We respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This new axiom enforces the maxitivity or the minitivity of the capacity without requiring the same property for the functional. It 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 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 to justify possibility and necessity measures. The axiomatization of these criteria for decision under uncertainty in the setting of preference relations among acts is also discussed. We show that the new axiom justifying possibilistic Choquet integrals can be expressed in this setting. In the case of Sugeno integral, we correct a characterization proof for an existing set of axioms on acts, and study an alternative set of axioms based on the idea of non-compensation.

Item Type:Article
Additional Information:Fuzzy Logic and Applications, Selected Papers from the French Fuzzy Set Conferen Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at : https://www.sciencedirect.com/science/article/pii/S0165011417302695
Audience (journal):International peer-reviewed journal
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)
Other partners > Université Lumière-Lyon 2 (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:19 Jul 2019 09:42

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