H-FQL: A new reinforcement learning method for automatic hierarchization of fuzzy systems: An application to the route choice problem

This paper proposes a new approach of automatic hierarchization for monolithic fuzzy systems based on an extension of the fuzzy Q-learning method. This approach contributes to the reduction of the fuzzy rules base without recourse to expert knowledge. It suggests firstly a new technique of automatic structural hierarchization, which advocates the association of the most correlated input variables' pairs through the statistical study of the samples' base. It also proposes the auto-generation of rules' bases using an adaptation of the Fuzzy Q-Learning (FQL) to the Hierarchical Fuzzy Systems (HFS). Finally, we applied the proposed approach to hierarchize an adaptive monolithic fuzzy system dealing with the route choice problem.

I. Introduction

Standard fuzzy inference systems [1] [2] have been successfully used in several applications as approximation, classification, etc. However, the curse of dimensionality [3] is the bottleneck of these systems. It concerns the exponential growth of the rules base's dimension for systems with a high input variables' number. In case of input variables with membership functions, we need rules to cover the total input space. Several techniques as fuzzy rules interpolation [4], orthogonal least-squares [5], singular value decomposition [6], similarity analysis [7], etc. were proposed to deal with rules base's reduction. Since it has been introduced, the hierarchical fuzzy systems design [8] was also considered as one of these techniques. It permits the distribution of the knowledge incorporated into a monolithic Fuzzy Inference System (FIS) to well interconnected sub-systems.