A Multi-Agent Architecture for the Design of Hierarchical Interval Type-2 Beta Fuzzy System

This paper presents a new methodology for building and evolving hierarchical fuzzy systems. For the system design, a tree-based encoding method is adopted to hierarchically link low-dimensional fuzzy systems. Such tree structural representation has by nature a flexible design offering more adjustable and modifiable structures. The proposed hierarchical structure employs a type-2 beta fuzzy system to cope with the faced uncertainties, and the resulting system is called the hierarchical interval type-2 beta fuzzy system (HT2BFS). For the system optimization, two main tasks of structure learning and parameter tuning are applied. The structure learning phase aims to evolve and learn the structures of a population of the HT2BFS in a multi-objective context taking into account the optimization of both the accuracy and the interpretability metrics. The parameter tuning phase is applied to refine and adjust the parameters of the system. To accomplish these two tasks in the most optimal way, we further employ a multi-agent architecture to provide both a distributed and a cooperative management of the optimization tasks. Agents are divided into two different types based on their functions: a structure agent and a parameter agent. The main function of the structure agent is to perform a multi-objective evolutionary structure learning step by means of the multi-objective immune programming algorithm. The parameter agents have the function of managing different hierarchical structures simultaneously to refine their parameters by means of the hybrid harmony search algorithm. In this architecture, agents use cooperation and communication concepts to create high-performance HT2BFSs. The performance of the proposed system is evaluated by several comparisons with various state-of-the-art approaches on noise-free and noisy time series prediction datasets and regression problems. The results clearly demonstrate a great improvement in accuracy rate, convergence speed, and the number of used rules as compared to other existing approaches.