Robust Methodology for Characterizing System Response to Damage: A Subjective (Fuzzy) Partial Ordered Modification of the Traditional Utility-Probability Scheme

To describe the response of engineering complex systems to various damage mechanics, engineers have traditionally use number-valued utilities to describe the results of different possible outcomes, and (number-valued) probabilities (often, subjective probabilities) to describe the relative frequency of different outcomes. This description is based on the assumption that experts can always make a definite preference between two possible outcomes, i.e., that the set of all outcomes is linearly (totally) ordered. In practice, experts often cannot make a choice, their preference is only a partial order. In this paper, we describe a new approach based on partial order.