Fuzzy alpha-cut vs. Monte Carlo techniques in assessing uncertainty in model parameters

This paper presents a comparison of two methods of analysis of uncertainty arising from uncertain model parameters. The first method is Monte Carlo simulation that treats parameters as random variables bound to a given probabilistic distribution and evaluates the distribution of the resulting output. The second one is fuzzy logic-based alpha-cut analysis in which uncertain parameters are treated as fuzzy numbers with given membership functions. Both techniques are tested on a model of ground water contaminant transport where the decay rate of the contaminant is considered to be uncertain. In order to provide a basis for comparison between these two approaches, the shapes of the membership function used in the fuzzy alpha-cut method is the same as the shape of the probability density function used in the Monte Carlo simulations. The analysis indicates that both methods give similar results provided that the correlation distance of the decay rate is assumed to be infinite. However, particular details of the analysis steps, computation time and representation of uncertainty are different, which may lead to the choice of one method or another depending on the nature of the problem.