An information theoretic approach to generating fuzzy hypercubes for if-then classifiers

Abstract

In this paper, a framework for automatic generation of fuzzy membership functions and fuzzy rules from training data is proposed. The main focus of this paper is designing fuzzy if-then classifiers; however the proposed method can be employed in designing a wide range of fuzzy system applications. After the fuzzy membership functions are modeled by their supports, an optimization technique, based on a multi-objective real coded genetic algorithm with adaptive cross over and mutation probabilities, is implemented to find near optimal supports. Employing interpretability constraint in parameter representation and encoding, we ensure that the generated fuzzy membership function does have a semantic meaning. The fitness function of the genetic algorithm, which estimates the quality of the generated membership functions, consists of two elements: (i) the Shannon entropy and mutual information measures to measure diversity of the data distribution in a hypercube; and (ii) the number of generated fuzzy rules addressing the measure of compactness of the fuzzy system. Finally membership functions are tuned to yield optimal classifier hypercubes, which represent the predictivity and discriminating power of the classifier. Fuzzy rules of the classifier are derived from the optimal hypercubes. Using the proposed approach to designing fuzzy if-then classifiers, we are also able to evaluate the generated membership functions and compare the results with that of other techniques which have been previously reported in the literature.Using the experimental result, we show that the proposed approach outperforms other techniques in low resolutions. It means that theproposed approach can achieve satisfying result with lower complexity.