Bayesian logical-probabilistic model of fuzzy inference: stages of conclusions obtaining and defuzzification

The article presents the Bayesian logical-probabilistic model of fuzzy inference, which differs from the traditionally used model at the content of the stages of the conclusions obtaining, and defuzzification. The proposed model of fuzzy inference is based on the application of the apparatus of probabilistic logic and Bayes formula. The set of fuzzy implication rules is transformed into a set of probabilistic logical functions, the arguments of which are values of membership functions of the input linguistic variables and the calculated values are used as conditional probabilities in determining the posterior distribution on the set of hypotheses corresponding to the values of the output linguistic variable. The resulting posterior probability distribution is used for defuzzification of the output linguistic variable value. The features of the proposed method of defuzzification are revealed and specified in comparison with the traditionally used approach. The distinctive properties and effectiveness of the proposed Bayesian logical-probabilistic model of fuzzy inference are shown in the examples.