Fuzzy If-Then Rules for Pattern Classification

Abstract

This chapter illustrates how fuzzy if-then rules can be used for pattern classification problems. First we describe a heuristic method for automatically generating fuzzy if-then rules for pattern classification problems from training patterns. The heuristic method uses a simple fuzzy grid for partitioning a pattern space into fuzzy subspaces. A fuzzy if-then rule is generated in each fuzzy subspace. Using the heuristic rule generation method, we examine some basic aspects of fuzzy rule-based classification systems such as the shape of membership functions, the definition of the compatibility grade, and the choice of a fuzzy reasoning method. Next we describe a fuzzy rule selection method for designing compact fuzzy rule-based systems with high classification ability. A small number of fuzzy if-then rules are selected from a large number of candidate rules by a genetic algorithm. Finally we describe two genetics-based machine learning algorithms for designing fuzzy rule-based systems for high-dimensional pattern classification problems. In those methods, fuzzy rule-based systems are evolved by genetic operations such as selection, crossover, and mutation. Simulation results on some well-known data sets are shown for illustrating our approaches to the design of fuzzy rule-based systems.