Evolutionary optimization of fuzzy systems using chained possibilistic rule graph encoding

Abstract

Fuzzy systems have been utilized and developed in many application fields and proven their usefulness for their unique feature that they solve the given problem with human understandable linguistic rules. As the design of a fuzzy system requires human experts`` knowledge which frequently becomes expensive and difficult, designing a fuzzy system solely based on relevant data by some optimization methods has been the main issue in literature. Especially, evolutionary algorithms receive much attention due to their vigorous and comprehensive optimization capabilities. Solving fuzzy system design problems using evolutionary algorithms demands three factors: an encoding scheme which can efficiently encode/decode candidate fuzzy systems into/from chromosomes, evaluation criteria which can guide candidate solutions into promising directions, and evolutionary operations which can evolve the given chromosomes into better form of solutions so that better fuzzy systems can be found as evolution proceeds. At the same time, those three factors should be designed considering three aspects of fuzzy systems: performance, compactness, and interpretability. This thesis proposes an automatic method to design fuzzy systems considering those requirements. The proposed method solves the fuzzy system design problem as a multi objective parameter optimization problem. For this purpose, this thesis firstly proposes a chained possibilistic rule graph encoding scheme which interpret premises of a fuzzy system as a graph. Vertices and edges of the chained possibilistic rule graph represents parameters of antecedent membership functions and structure variation, which enables simultaneous optimization of structure and parameters of fuzzy systems effectively. Secondly, five evaluation criteria which consider performance, compactness, and interpretability of fuzzy systems are developed. Especially, two new measures which constrain distribution of antecedent membership functions in phenoty...