V. V. Borisov, A. Yu. Belozersky

Various aspects of the risk analysis of making decisions are considered on the basis of fuzzy Bayesian networks. The risk of the making decision is defined as probability (opportunity) of occurrence of one event at approach of other event. Classification of methods of introduction of fuzziness in a Bayesian network is offered depending on character of the used information and features of decided tasks of the risk analysis: complement of the Bayesian rule with membership functions of corresponding values of variables; replacement of values of probabilities by fuzzy sets (terms of linguistic variables), and operations with crisp values - on operations S-and Т-norms with fuzzy sets; replacement of values of probabilities by fuzzy numbers, and usual operations - on the expanded operations above indistinct numbers. The fuzzy inference with use fuzzy Bayesian networks based on use of expanded arithmetic operations above fuzzy numbers is considered. The technique of construction and use of fuzzy Bayesian networks for the risk analysis is submitted. The contensive examples showing a technique of inference on the basis of fuzzy Bayesian networks are considered. Results of the risk analysis of investment decisions with use of this approach are received.