Automatic Construction of Fuzzy Rule-Based Systems: A trade-off between complexity and accuracy maintaining interpretability

Abstract

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. An important characteristic that distinguishes fuzzy systems from other techniques in this area is their transparency and interpretability. Especially in the construction of a fuzzy system from a set of given training examples, little attention has been paid to the analysis of the trade-off between complexity and accuracy maintaining the interpretability of the final fuzzy system. In this chapter a systematic data based approach is proposed to determine fuzzy system structure and learning its parameters. In particular, two fundamental issues concerning fuzzy system modeling are addressed: fuzzy rule parameter optimization and the identification of system structure (i.e. the number of membership functions and fuzzy rules), taking always in mind the transparency of the obtained rule-base. This chapter presents a reliable method to obtain the structure of a complete rule-based fuzzy system for a specific approximation accuracy of the training data, i.e., it can decide which input variables must be taken into account in the fuzzy system and how many membership functions are needed in every selected input variable in order to reach the approximation target with the minimum number of parameters. The main criterion of comparison of all fuzzy systems obtained is their performance, measured as the accuracy of the model, versus complexity (number of parameters). Since determining which configuration has optimum characteristics is a clear example of fuzzy decisiontaking, in this chapter the preferences of the human operator (end user) concerning the two conflicting objectives considered in evaluating the fuzzy system are translated into fuzzy rules.