Entropy of bi-capacities |
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Authors: | Ivan Kojadinovic Jean-Luc Marichal |
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Affiliation: | 1. LINA CNRS FRE 2729, Site école polytechnique de l’Université de Nantes, Rue Christian Pauc, 44306 Nantes, France;2. Applied Mathematics Unit, University of Luxembourg, 162A, avenue de la Faïencerie, L-1511 Luxembourg, Grand Duchy of Luxembourg |
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Abstract: | In the context of multicriteria decision making whose aggregation process is based on the Choquet integral, bi-capacities can be regarded as a natural extension of capacities when the underlying evaluation scale is bipolar. The notion of entropy, recently generalized to capacities to measure their uniformity, is now extended to bi-capacities. We show that the resulting entropy measure has a very natural interpretation in terms of the Choquet integral and satisfies many natural properties that one would expect from an entropy measure. |
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Keywords: | Multicriteria decision making Bi-capacity Choquet integral Entropy |
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