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Generalized qualitative Sugeno integrals

Dubois, Didier and Prade, Henri and Rico, Agnès and Teheux, Bruno Generalized qualitative Sugeno integrals. (2017) Information Sciences, 415 - 416. 429-445. ISSN 0020-0255

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Official URL: https://doi.org/10.1016/j.ins.2017.05.037

Abstract

Sugeno integrals are aggregation operations involving a criterion weighting scheme based on the use of set functions called capacities or fuzzy measures. In this paper, we define generalized versions of Sugeno integrals on totally ordered bounded chains, by extending the operation that combines the value of the capacity on each subset of criteria and the value of the utility function over elements of the subset. We show that the generalized concept of Sugeno integral splits into two functionals, one based on a general multiple-valued conjunction (we call integral) and one based on a general multiple-valued implication (we call cointegral). These fuzzy conjunction and implication connectives are related via a so-called semiduality property, involving an involutive negation. Sugeno integrals correspond to the case when the fuzzy conjunction is the minimum and the fuzzy implication is Kleene-Dienes implication, in which case integrals and cointegrals coincide. In this paper, we consider a very general class of fuzzy conjunction operations on a finite setting, that reduce to Boolean conjunctions on extreme values of the bounded chain, and are non-decreasing in each place, and the corresponding general class of implications (their semiduals). The merit of these new aggregation operators is to go beyond pure lattice polynomials, thus enhancing the expressive power of qualitative aggregation functions, especially as to the way an importance weight can affect a local rating of an object to be chosen.

Item Type:Article
Additional Information:https://www.sciencedirect.com/science/article/pii/S0020025516318977
HAL Id:hal-01919017
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 > University of Luxembourg (LUXEMBOURG)
Laboratory name:
Funders:
ANR-11-LABX-0040-CIMI (Centre International de Mathématiques et d’Informatique) within the program ANR-11-IDEX-0 0 02-02
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Deposited By: IRIT IRIT
Deposited On:18 Oct 2018 13:52

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