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Residuated variants of Sugeno integrals: Towards new weighting schemes for qualitative aggregation methods

Dubois, Didier and Prade, Henri and Rico, Agnés Residuated variants of Sugeno integrals: Towards new weighting schemes for qualitative aggregation methods. (2016) Information Sciences, vol. 329. pp. 765-781. ISSN 0020-0255

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Official URL: https://doi.org/10.1016/j.ins.2015.09.034

Abstract

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.

Item Type:Article
Additional Information:Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Information Sciences (ISSN : 0020-0255) website : http://www.sciencedirect.com/science/article/pii/S002002551500688X
HAL Id:hal-01538305
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)
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Deposited By: IRIT IRIT
Deposited On:07 Jun 2017 08:58

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