# A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

@article{Grabisch2008ADO, title={A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid}, author={Michel Grabisch and Christophe Labreuche}, journal={Annals of Operations Research}, year={2008}, volume={175}, pages={247-286} }

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields…

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## 444 Citations

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

- Computer ScienceAnn. Oper. Res.
- 2010

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet…

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The Choquet integral is employed for the generalization of the Partial Goals Method and the theory is demonstrated on an example implemented in a new software capable of dealing with multiple criteria evaluation via the fuzzified Choquette integral.

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This paper will compute the probability that a recommendation to a decision maker could only been obtained with the Choquet integral and not with a weighted sum, and shows that this probability tends to one.

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New computational models based on mathematical programming to optimize the Choquet integral on implicit sets exploiting the vertices of the core of the convex capacity are proposed, combined with a constraint generation algorithm.

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The proposed method can be considered as an extension of the existing methods, and can obtain smaller deviations and better overall evaluations of alternatives.

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This paper proposes two types of optimization problems that allow identifying the parameters of a 2-additive bi-capacity such that the inferred bipolar Choquet integral is consistent with the given examples as much as possible.

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The Choquet integral with respect to a fuzzy measure is presented as an alternative to the weighted sum for aggregating criteria and the Shapley value and the interaction index are presented.

Partially Bipolar Choquet Integrals

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This work investigates Choquet-like aggregation models that are fully bipolar only with respect to certain criteria and whose number of parameters is much lower than that of the bipolar Choquet integral.

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In this paper, we explore a new way to learn an aggregation operator for fusion based on a combination of one or more labeled training data sets and information from one or more experts. One problem…

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A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

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The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet…

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