FRULER: Fuzzy Rule Learning through Evolution for Regression

Abstract: In regression problems, the use of TSK fuzzy systems is widely extended due to the precision of the obtained models. Moreover, the use of simple linear TSK models is a good choice in many real problems due to the easy understanding of the relationship between the output and input variables. In this paper we present FRULER, a new genetic fuzzy system for automatically learning accurate and simple linguistic TSK fuzzy rule bases for regression problems. In order to reduce the complexity of the learned models while keeping a high accuracy, the algorithm consists of three stages: instance selection, multi-granularity fuzzy discretization of the input variables, and the evolutionary learning of the rule base that uses the Elastic Net regularization to obtain the consequents of the rules. Each stage was validated using 28 real-world datasets and FRULER was compared with three state of the art enetic fuzzy systems. Experimental results show that FRULER achieves the most accurate and simple models compared even with approximative approaches.