Diagnosing with a hybrid fuzzy–Bayesian inference approach

Abstract

A diagnosis based on Bayesian theory requires knowledge of the a priori and conditional probabilities of the states of the system being diagnosed. The a priori probabilities are frequently provided nowadays by the manufacturers of these systems. In turn, the probabilities of conditional observations are, as a rule, not available. The question arises as to whether and under what conditions it is possible to substitute conditional probabilities with some aggregate obtainable on the grounds of fuzzy logic. This article responds to this question by proposing a hybrid approach with novelty characteristics in both theoretical and practical terms. In the initial phase of the deliberations, it was concluded that the fundamental difference between Bayesian and fuzzy approaches is that the fuzzy approach considers the uncertainty and lack of precision of observations but overlooks the frequency of observations, and the opposite is true of the Bayesian approach. It therefore seems reasonable to seek the hybridization of both methods so that the Bayesian approach carrying the information regarding the subjective probabilities of faults can be applied in practice. To this end, it has been shown that the probability of a conditional observation can be estimated by calculating the degree of truth of the premise for that observation in the state-specific fuzzy rule. The reminder is devoted to presenting numerical and simulation examples illustrating and verifying the proposed approach.