## $$p$$-symmetric bi-capacities.(English)Zbl 1249.28021

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,$$\ldots$$) into subsets whose elements are all indifferent for the decision maker.

### MSC:

 28E05 Nonstandard measure theory 28E10 Fuzzy measure theory 03H05 Nonstandard models in mathematics 28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures

### Keywords:

bi-capacity; bipolar scales; $$p$$-symmetry
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### References:

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