A Generalization of the Utility Theory using a Hybrid Idempotent–Probabilistic Measure

There is given an overview on the results related to the generalization of the decision theory to non probabilistic uncertainty based on the characterization of the families of operations involved in generalized mixtures. It turns out that this is based on a previous result on the characterization of the pair of continuous t-norm T and t-conorm S such that the former is conditionally distributive over the latter. What is obtained is a family of mixtures that combine probabilistic and idempotent (possibilistic) mixtures via a threshold and the corresponding pseudo-additive hybrid idempotent-probabilistic measure satisfies also all other required conditions.