Geodesic
$p$-symmetric bi-capacities
Kybernetika, Tome 40 (2004) no. 4, pp. 421-440 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order $3^n$, instead of $2^n$ for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of $p$-symmetric bi- capacities, in the same spirit as for $p$-symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature, individuals,...) into subsets whose elements are all indifferent for the decision maker.
Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order $3^n$, instead of $2^n$ for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of $p$-symmetric bi- capacities, in the same spirit as for $p$-symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature, individuals,...) into subsets whose elements are all indifferent for the decision maker.
Classification : 03E72, 03H05, 28A12, 28C05, 28E05, 28E10
Keywords: bi-capacity; bipolar scales; $p$-symmetry 
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Miranda, Pedro; Grabisch, Michel. $p$-symmetric bi-capacities. Kybernetika, Tome 40 (2004) no. 4, pp. 421-440. http://geodesic.mathdoc.fr/item/KYB_2004_40_4_a1/

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