Article (Scientific journals)
Generalized qualitative Sugeno integrals
Dubois, Didier; Prade, Henri; Rico, Agnès et al.
2017In Information Sciences, 415-416, p. 429-445
Peer reviewed


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Keywords :
qualitative integrals; Sugeno integrals
Abstract :
[en] 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.
Disciplines :
Author, co-author :
Dubois, Didier;  Université Paul Sabatier - Toulouse 3 - UPS > IRIT
Prade, Henri;  Université Paul Sabatier - Toulouse 3 - UPS > IRIT
Rico, Agnès;  Université Claude Bernard - Lyon 1 - UCLB > ERIC
Teheux, Bruno ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
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Title :
Generalized qualitative Sugeno integrals
Publication date :
Journal title :
Information Sciences
Volume :
Pages :
Peer reviewed :
Peer reviewed
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since 18 July 2017


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