Choquet weak convergence of capacity functionals of random sets

Authors:
Ding Feng;Hung T. Nguyen
Affiliations:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-8001, USA;Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-8001, USA
Venue:
Information Sciences: an International Journal
Year:
2007

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Abstract

The results in this paper are about the convergence of capacity functionals of random sets. The motivation stems from asymptotic aspects in inference and decision-making with coarse data in biostatistics, set-valued observations, as well as connections between random sets with several emerging uncertainty calculi in intelligent systems such as fuzziness, belief functions and possibility theory. Specifically, we study the counter-part of Billingsley's Portmanteau Theorem for weak convergence of probability measures, namely, convergence of capacity functionals of random sets in terms of Choquet integrals.