Decision making over necessity measures through the Choquet integral criterion

We consider a decision maker who ranks necessity measures according to their Choquet's expected utilities. We provide an axiomatization of such preferences. If the decision maker follows our set of axioms then there exists a fuzzy set such that any necessity measure can be reduced to a bet on being perfectly informed of the state which occurs or being totally ignorant, where the degree of information he will get is given by its Choquet expectation of the fuzzy set. This approach is similar to von Neuman and Morgenstern's method under risk where a rational decision maker should evaluate a lottery according to its expected utility. (c) 2006 Elsevier B.V. All rights reserved.