Fuzzy functions to select an optimal action in decision theory

In decision under uncertainty, we aim at finding a scoring procedure to determine an optimal decision without prior knowledge on the actual state of the world. It is well known that the probability approach to this problem leads to paradoxes, that are related to independence properties required on the preferences. This naturally leads us to drop additivity and therefore, replace probabilities with fuzzy measures. The aim of this paper is to present several benefit functions to identify optimal actions, in the fuzzy measure and fuzzy logic perspective.