Fuzzy Bayesian analysis with continuous-valued evidence

Bayesian methods provide a formalism for reasoning about partial beliefs under conditions of uncertainty. In this formalism, propositions are given numerical parameters signifying the degree of belief accorded them under some body of knowledge, and the parameters are combined and manipulated according to the rules of probability. In many situations, the evidence may not be described by a single atomic proposition, instead it is multi-valued. The values could be discrete, continuous, or fuzzy. Recently, fuzzy Bayesian theorem has been widely applied to determine the reliability of a structure. In the theorem, the conditional probability of a fuzzy evidence is computed based on the conditional density function of the continuous-valued evidence. However, the conditional density function is not available in many situations, instead, the conditional probability of the fuzzy support value is easier to be obtained from experience. In this paper, a new mechanism is introduced to estimate the conditional density function of a continuous-valued evidence given the conditional probability of the fuzzy support values. Experiments are conducted to evaluate the accuracy of the estimation using the new technique