An Evolutionary Fuzzy Classifier with Adaptive Ellipsoids

A fuzzy classifier using multiple ellipsoids approximating decision regions for classification is designed in this paper. We define a fuzzy rule to represent an ellipsoid decision region. An algorithm called Gustafson-Kessel Algorithm (GKA) with an adaptive distance norm based on covariance matrices of prototype data is adopted to learn the ellipsoids. GKA is able to adapt the distance norm to the prototype data except that the sizes of ellipsoids need to be determined a priori. To overcome GKA´s inability to determine appropriate size of ellipsoid, the genetic algorithm (GA) is applied to learn the size of ellipsoid. With GA combined with GKA, the proposed method outperforms the benchmark algorithms as well as algorithms in the field.