Geodesic
$p$-symmetric bi-capacities
Kybernetika, Tome 40 (2004) no. 4, p. [421]

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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.
Classification : 03E72, 03H05, 28A12, 28C05, 28E05, 28E10
Keywords: bi-capacity; bipolar scales; $p$-symmetry 
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     author = {Miranda, Pedro and Grabisch, Michel},
     title = {$p$-symmetric bi-capacities},
     journal = {Kybernetika},
     pages = {[421]},
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     volume = {40},
     number = {4},
     year = {2004},
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     zbl = {1249.28021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2004__40_4_a1/}
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Miranda, Pedro; Grabisch, Michel. $p$-symmetric bi-capacities. Kybernetika, Tome 40 (2004) no. 4, p. [421]. http://geodesic.mathdoc.fr/item/KYB_2004__40_4_a1/