Ranking probability measures by inclusion indices in the case of unknown utility function.
This paper gives a way of analyzing decisions in the case of unknown utility function, or more precisely, when we know only a linear order on an income space. It is shown that in this situation, decisions and corresponding probability measures are partially ordered, and this order is identical to the inclusion relation of comonotone fuzzy sets. It enables us to use inclusion indices of fuzzy sets to analyze the comparability of decisions. To do this, we introduce an inclusion index having properties, which are close to ones of the classical expected utility.