Fuzzy decision making using the imprecise Dirichlet model

In most applications, probabilities of states of nature in decision making are not known exactly due to a lack of complete information. If the available information is represented by a small number of statistical data, Walley’s imprecise Dirichlet model may be regarded as a tool for determining interval probabilities of states of nature. It turns out that the resulting expected utilities constitute fuzzy sets and the initial decision problem is reduced to a fuzzy decision problem. A numerical example illustrates the proposed approach to solving decision problems under the scarce information about states of nature. The approach is compared with ?-contaminated (robust) models. This approach can also be applied to construction of fuzzy sets on the basis of statistical observations.