Decision Making by Hybrid Probabilistic-Possibilistic Utility Theory

Abstract

It is presented an approach to decision theory based upon nonprobabilistic uncertainty. There is an axiomatization of the hybrid probabilistic-possibilistic mixtures based on a pair of triangular conorm and triangular norm satisfying restricted distributivity law, and the corresponding non-additive S-measure. This is characterized by the families of operations involved in generalized mixtures, based upon a previous result on the characterization of the pair of continuous t-norm and t-conorm such that the former is restrictedly distributive over the latter. The obtained family of mixtures combines probabilistic and idempotent (possibilistic) mixtures via a threshold.

Key words: Decision making, Utility theory, Possibilistic mixture, Hybrid probabilistic-possibilistic mixture, Triangular norm, Triangular conorm, Pseudo-additive measure.
JEL: C44, L97.