Evolutionary domain covering of an inference system for function approximation

Abstract

Many interesting and important problems related to the analysis of large numerical data can be formulated as a problem of approximating a function from a set of sample points. Any approximation method should provide minimum error at the given data samples and also should approximate values for other points of the function's domain.

In this paper a method leading to clustering of multidimensional large numerical data is proposed. The method uses a problem-specific evolutionary algorithm which partitions the data space into clusters and forms membership functions of the fuzzy sets involved in the premise parts of the fuzzy rules. The proposed algorithm has a two-stage hierarchial organization. For the first stage, an evolutionary algorithm is used, where an individual in the population represents a cluster of data samples. Three specialized operators are defined to operate on such individuals. During the second stage, a greedy algorithm is used for finding a near-optimum covering.