Representing Uncertainty by Probability and Possibility: What's the Difference?

Uncertain parameters in modeling are usually represented by probability distributions reflecting either the objective uncertainty of the parameters or the subjective belief held by the model builder. This approach is particularly suited for representing the statistical nature or variance of uncertain parameters. Monte Carlo simulation is readily used for practical calculations. However, an alternative approach is offered by possibility theory making use of possibility distributions such as intervals and fuzzy intervals. This approach is well suited to represent lack of knowledge or imprecision concerning uncertain parameters. Interval arithmetic and global optimization is used for practical calculations. The two alternative approaches are based on quite different concepts and mathematical principles and also yield quite different results when applied to identical numerical uncertain data. This is demonstrated by a number of numerical examples.