Comparison of probabilistic and fuzzy set methods for designing under uncertainty

Abstract

The objective of this paper is to compare probabilistic models and fuzzy set models for design against uncertainty when there is limited information about the statistics of the uncertainty or modeling error. First, we compare the axioms of probabilistic and fuzzy set methods and the rules governing the arithmetic operations that these methods use. Then, we compare the two methods in designing for maximum safety under a given budget. In general, if there is sufficient information to build accurate probabilistic models of uncertainties, probabilistic methods are better than fuzzy set methods. On the other hand, fuzzy set methods can be better if little information is available. One reason is that it is easier to identify the most conservative fuzzy set model than the most conservative probabilistic model that is consistent with the available information.