Non-monotonic fuzzy measures and the Choquet integral
Fuzzy Sets and Systems
The concave integral over large spaces
Fuzzy Sets and Systems
On the continuity of the concave integral
Fuzzy Sets and Systems
Hesitant fuzzy geometric Bonferroni means
Information Sciences: an International Journal
Choquet integral on the real line as a generalization of the OWA operator
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
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A model for a Choquet integral for arbitrary finite set systems is presented. The model includes in particular the classical model on the system of all subsets of a finite set. The general model associates canonical non-negative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system, which are then extended to arbitrary valuations on the set system. It is shown that the general Choquet integral can be computed by a simple Monge-type algorithm for so-called intersection systems, which include as a special case weakly union-closed families. Generalizing Lovasz' classical characterization, we give a characterization of the superadditivity of the Choquet integral relative to a capacity on a union-closed system in terms of an appropriate model of supermodularity of such capacities.