Title: Fuzzy decision making using the imprecise Dirichlet model

Authors: Lev V. Utkin; Yulia A. Zhuk

Addresses: Department of Industrial Control and Automation, St. Petersburg State Forest Technical University, Institutsky per. 5, 194021 St. Petersburg, Russia ' Department of Computer Science, St. Petersburg State Forest Technical University, Institutsky per. 5, 194021 St. Petersburg, Russia

Abstract: In most applications, probabilities of states of nature in decision making are not known exactly owing 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 for the construction of fuzzy sets on the basis of statistical observations.

Keywords: decision problems; fuzzy sets; robust modelling; imprecise Dirichlet model; expected utilities; fuzzy decision making; uncertainty.

DOI: 10.1504/IJMOR.2013.050513

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.1, pp.74 - 90

Published online: 31 Mar 2014 *

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