Fuzzy probabilities

摘要

The conventional approaches to decision analysis are based on the assumption that the probabilities which enter into the assessment of the consequences of a decision are known numbers. In most realistic settings, this assumption is of questionable validity since the data from which the probabilities must be estimated are usually incomplete, imprecise or not totally reliable.In the approach outlined in this paper, the probabilities are assumed to be fuzzy rather than real numbers. It is shown how such probabilities may be estimated from fuzzy data and a basic relation between joint, conditional and marginal fuzzy probabilities is established. Manipulation of fuzzy probabilities requires, in general, the use of fuzzy arithmetic, and many of the properties of fuzzy probabilities are simple generalizations of the corresponding properties of real-valued probabilities.