CHOQUET INTEGRALS AND NATURAL EXTENSIONS OF LOWER PROBABILITIES

Both the Choquet integral with respect to monotone set functions and t he natural extensions of lower probabilities are generalizations of th e Lebesgue integral with respect to sigma-additive measures. The relat ion between these generalizations is investigated. We show that the Ch oquet integral with respect to a belief measure is always greater than or equal to the corresponding natural extension. Also, we compare som e concepts introduced in the theory of imprecise probabilities with co ncepts established in fuzzy measure theory capacity theory, and Dempst er-Shafer theory. (C) 1997 Elsevier Science Inc.