Decision Making for Robust Resilient Systems

Robust and resilient interconnected structures rely on decision procedures, both under uncertainty and multicriteria. 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. In multicriteria decision making, the state of the world is known but we aim at ranking alternatives defined over a multidimensional set. Therefore, the problem is to find an appropriate aggregation procedure. In practical applications, we have to deal with decision problems where the state of the world is not known, and the alternatives are multidimensional. It is well known that the probability approach to these 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 non-additive measures. The aim of this paper is to present several benefit functions to identify optimal actions, in the fuzzy measure and fuzzy logic perspective.