Fuzzy modeling incorporated with fuzzy D-S theory and fuzzy naive bayes

Abstract

In fuzzy model, the consequent of fuzzy rule is often determined with degrees of belief or credibility because of vague information originating from evidence not strong enough and "lack of specificity". In this paper, we present a fuzzy model incorporated with fuzzy Dempster-Shafer Theory. The consequent of fuzzy rule is not fuzzy propositions, but fuzzy Dempster-Shafer granules. The salient aspect of the work is that a very simplified analytic output of fuzzy model which is a special case of Sugeno-type fuzzy model is achieved when all fuzzy sets in fuzzy partition of the output space have the same power (the area under the membership function), and the determination of basic probability assignments associated with fuzzy Dempster-Shafer belief structure using fuzzy Naive Bayes. The construction method of fuzzy Naive Bayes and an learning strategy generating fuzzy rules from training data are proposed in this paper. A well-known example about time series prediction is tested, the prediction results show that our fuzzy modeling is very efficient and has strong expressive power to represent the complex system with uncertain situation. © Springer-Verlag Berlin Heidelberg 2004.