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Commuting double Sugeno integrals

Dubois, Didier and Fargier, Hélène and Rico, Agnès Commuting double Sugeno integrals. (2019) International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 27 (Supplement). 1-38. ISSN 0218-4885

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Official URL: https://doi.org/10.1142/S0218488519400014

Abstract

In decision problems involving two dimensions (like several agents in uncertainty) the properties of expected utility ensure that the result of a two-stepped procedure evaluation does not depend on the order with which the aggregations of local evaluations are performed (e.g., agents first, uncertainty next, or the converse). We say that the aggregations on each dimension commute. In a previous conference paper, Ben Amor, Essghaier and Fargier have shown that this property holds when using pessimistic possibilistic integrals on each dimension, or optimistic ones, while it fails when using a pessimistic possibilistic integral on one dimension and an optimistic one on the other. This paper studies and completely solves this problem when more general Sugeno integrals are used in place of possibilistic integrals, leading to double Sugeno integrals. The results show that there are capacities other than possibility and necessity measures that ensure commutation of Sugeno integrals. Moreover, the relationship between two-dimensional capacities and the commutation property for their projections is investigated.

Item Type:Article
Additional Information:The definitive version is available at: https://www.worldscientific.com/doi/10.1142/S0218488519400014
HAL Id:hal-02940966
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 - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (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 On:31 Aug 2020 08:40

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