A characterization of the 2-additive Choquet integral through cardinal information

In the context of multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.MCDA; Choquet integral; 2-Additive capacity; MACBETH methodology

Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process

We propose to extend the aggregation scheme of Saaty’s AHP, from the stan- dard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the con- sistency case. In the general inconsistency case, however, the new aggregation scheme based on Choquet integration tends to attenuate (resp. emphasize) the priority values of the criteria with higher (resp. lower) average inconsistency with the remaining criteria.Aggregation Functions, Multiple Criteria Analysis, AHP, Inconsintency, non-additive measures, Choquet integral, and Shapley values.

Using MACBETH with the choquet integral fundamentals to model interdependencies between elementary concerns in the context of risk management

Effective risk management typically requires the evaluation of multiple consequences of different sources of risk, and multicriteria value models have been used for that purpose. The value of mitigating a risk impact is often considered by risk managers as dependent on the levels of other impacts, therefore there is a need for procedures to identify and model these interactions within a value measurement framework. The Choquet Integral (CI) has been used for this purpose, and several studies in the performance measurement literature have combined the 2-additive CI operator with the MACBETH approach to model interdependencies in real contexts. In this paper, we propose an alternative procedure to model interdependencies and determine the CI parameters from one single MACBETH global matrix. The procedure is illustrated with the construction of a descriptor of impacts to evaluate the risk impacts at ALSTOM Power. The paper further explains the questioning protocol to apply the proposed procedure, as well as how decision-makers can interpret the CI parameters

A characterization of the 2-additive Choquet integral through cardinal information

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