Knowledge Embedded Bayesian MA Fuzzy System

The most distinctive characteristic of fuzzy system is its high interpretability. But the fuzzy rules obtained by classical cluster based fuzzy systems commonly need to cover all features of input space and often overlap each other. Specially, when facing the high-dimension problem, the fuzzy rules often become more sophisticated because of too much features involved in antecedent parameters. In order to overcome these shortcomings, based on the Bayesian inference framework, knowledge embedded Bayesian Mamdan-Assilan type fuzzy system (KE-B-MA) is proposed by focusing on the Mamdan-Assilan (MA) type fuzzy system. First, the DC (dont care) approach is incorporated into the selection of fuzzy membership centers and features of input space. Second, in order to enhance the classification performance of obtained fuzzy systems, KE-B-MA learns both antecedent and consequent parameter of fuzzy rules simultaneously by a Markov chain Monte Carlo (MCMC) method, and the obtained parameters can be guaranteed to be global optimal solutions. The experimental results on a synthetic dataset and several UCI machine datasets show that the classification accuracy of KE-B-MA is comparable to several classical fuzzy systems with distinctive ability of providing explicit knowledge in the form of interpretable fuzzy rules. Rather than being rivals, fuzziness in KE-B-MA and probability can be well incorporated.