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Keywords:
bi-capacity; bipolar scales; $p$-symmetry
bi-capacity; bipolar scales; $p$-symmetry
Summary:
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.
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