Decision problems usually involve two important sources of uncertainty: randomness and fuzziness in real life. In this paper a mathematical model is developed to deal with dynamic Bayesian decision problems affected by uncertainties. The model can handle multi-step uncertainty decision problems involving randomness and fuzziness by a valuation-based system. The method uses linguistic variables to assess probabilities in the real-valued case, so a defuzzification method for the linguistic probability based on the concept of probability measure of fuzzy events is proposed. The decision valuations are described by triangular fuzzy sets. A fuzzy marginalization method based on fuzzy value comparison is proposed in the FVBS. A real world application example is provided to illustrate the method.
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