A quantile approach to integration with respect to non-additive measures

Authors:
Marta Cardin
Affiliations:
Department of Economics, University Cà Foscari of Venice, Venice, Italy
Venue:
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
Year:
2012

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Abstract

The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. We focus on the notion of quantile of a lattice-valued function which have several properties of its real-valued counterpart and we study a class of aggregation functionals that generalizes Sugeno integrals to the setting of complete lattices. Then we introduce in the real-valued case some classes of aggregation functionals that extend Choquet and Sugeno integrals by considering a multiple quantile model generalizing the approach proposed in [3].