Zy. Wang et Gj. Klir, CHOQUET INTEGRALS AND NATURAL EXTENSIONS OF LOWER PROBABILITIES, International journal of approximate reasoning, 16(2), 1997, pp. 137-147
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.