Some Links Between Decomposable Measures And Capacities Modeling Uncertainty Attitudes

Abstract

During those last years, the use of capacities has been extensively proposed to model attitudes towards uncertainty. Here we try to precise the links between some classes of capacities, namely between decomposable measures introduced by DUBOIS and PRADE and other measures as concave (resp: convex) capacities and distorted probabilities which appeared in two significant new models of non-additive expected utility theory (SCHMEIDLER, YAARI). It is shown that the most well-known decomposable measures prove to be distorted probabilities, and that any concave distortion of a probability is decomposable. The paper ends with successively characterizing decomposable measures which are concave distortions of probabilities, and ⊥ -decomposable measures (for triangular conorms ⊥. ) which are concave, since decomposable measures prove to be much more adapted to concavity than convexity.