Generation of a probabilistic fuzzy rule base by learning from examples

This study considers probabilistic fuzzy systems constructed using Mamdani probabilistic fuzzy rules. As a generalisation of deterministic fuzzy systems, Mamdani probabilistic fuzzy systems better model practical complex systems involving uncertainty because they combine the interpretability of fuzzy systems with the statistical properties of probabilistic systems. Using probabilistic fuzzy rules, both probabilistic uncertainty and linguistic ambiguity are handled simultaneously with a single framework. Considering that the information available often consists of a training set of input–output data pairs, a general method for generating Mamdani probabilistic fuzzy rule bases from numerical data pairs is presented. A fuzzy reasoning method is used on the generated probabilistic fuzzy rule base to derive a map leading from the input space to the output space, and a probabilistic fuzzy system is constructed. We use this probabilistic fuzzy modelling method for nonlinear regression analysis. The effectiveness of the proposed method is demonstrated by a comparison with similar regression techniques.