Combining Bayesian and logical-probabilistic approaches for fuzzy inference systems implementation

Abstract

In the paper, an original way to implement the fuzzy inference systems is considered. The proposed fuzzy inference model is based on usage of conjunction of probabilistic logic and Bayes’ formula at inference stage. For that preconditions of all the specified fuzzy production rules are transformed to the set of probabilistic functions. As the input probabilities, the values of membership functions of input linguistic variables terms are used. At that given set of production rules is reduced in the way that number of rules will be equal to number of terms of output linguistic variables. For that logic expressions of production preconditions are transformed to orthogonal DNFs. Calculated probability values are used as conditional probabilities in determining the posterior distributions on the set of hypotheses corresponding to values of the output linguistic variables. To determine the posterior probability distribution, we use the formula based on the Bayes’ formula. These posterior distributions are used at defuzzification stage for determining final output variable values, because they are calculated as expected values of corresponding random variables. The program implementation has allowed to estimate the proposed model effectiveness and to compare its results with results of traditionally used Mamdani and Sugeno fuzzy inference algorithms.