A Fast and Accurate Rule-Base Generation Method for Mamdani Fuzzy Systems

The problem of learning fuzzy rule bases is analyzed from the perspective of finding a favorable balance between the accuracy of the system, the speed required to learn the rules, and, finally, the interpretability of the rule bases obtained. Therefore, we introduce a complete design procedure to learn and then optimize the system rule base, called the precise and fast fuzzy modeling approach. Under this paradigm, fuzzy rules are generated from numerical data using a parameterizable greedy-based learning method called selection-reduction, whose accuracy-speed efficiency is confirmed through empirical results and comparisons with reference methods. Qualitative justification for this method is provided based on the coaction between fuzzy logic and the intrinsic properties of greedy algorithms. To complete the precise and fast fuzzy modeling strategy, we finally present a rule-base optimization technique driven by a novel rule redundancy index, which takes into account the concepts of the distance between rules and the influence of a rule over the dataset. Experimental results show that the proposed index can be used to obtain compact rule bases, which remain very accurate, thus increasing system interpretability.