Learning of fuzzy reference sets in nearest neighbor classification

We have already proposed a GA-based approach to the design of compact fuzzy nearest neighbor classifiers (H. Ishibuchi and T. Nakashima, 1998). We propose two learning algorithms for the fuzzy nearest neighbor classifiers: one is the learning of the certainty grade of each fuzzy if-then rule, and the other is the learning of the radius of its antecedent fuzzy set (i.e., the radius of the circular-cone type membership function). These two algorithms are based on a reward-punishment scheme. When a pattern is correctly classified, the certainty grade of the winner fuzzy if-then rule and/or the radius of its antecedent fuzzy set are increased. On the other hand, the certainty grade and/or the radius of the winner fuzzy if-then rule are decreased when a pattern is misclassified. We examined the learning algorithms by computer simulations on real-world pattern classification problems. We demonstrate that the performance of the fuzzy nearest neighbor classifiers is improved by the learning.