A Discrete Choquet Integral for Ordered Systems

Ulrich Faigle () and Michel Grabisch

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: 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 Lovász' 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.

Keywords: Choquet integral; belief function; measurability; set systems; Monge algorithm; supermodularity (search for similar items in EconPapers)
Date: 2011
New Economics Papers: this item is included in nep-cis
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00563926v1
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Published in Fuzzy Sets and Systems, 2011, 168 (1), pp.3-17. ⟨10.1016/j.fss.2010.10.003⟩

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Working Paper: A Discrete Choquet Integral for Ordered Systems (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-00563926

DOI: 10.1016/j.fss.2010.10.003

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