A Monge Algorithm for Computing the Choquet Integral on Set Systems
نویسندگان
چکیده
In works dealing with capacities (fuzzy measures) and the Choquet integral on finite spaces, it is usually considered that all subsets of the universe are measureable. Hence, all functions are integrable in the sense of Choquet. We consider the situation where some subsets are not measurable (not feasible), so that there are nonintegrable functions. Since this is a severe limitation in applications, we study how to extend the Choquet integral to any function. Our results mainly deal with the case where the set of feasible subsets is a distributive lattice. Keywords— Choquet integral, fuzzy measure, capacity, Monge algorithm, set system, distributive lattice
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