Automatic Design of Hierarchical Takagi–Sugeno Type Fuzzy Systems Using Evolutionary Algorithms

This paper presents an automatic way of evolving hierarchical Takagi-Sugeno fuzzy systems (TS-FS). The hierarchical structure is evolved using probabilistic incremental program evolution (PIPE) with specific instructions. The fine tuning of the if - then rule´s parameters encoded in the structure is accomplished using evolutionary programming (EP). The proposed method interleaves both PIPE and EP optimizations. Starting with random structures and rules´ parameters, it first tries to improve the hierarchical structure and then as soon as an improved structure is found, it further fine tunes the rules´ parameters. It then goes back to improve the structure and the rules´ parameters. This loop continues until a satisfactory solution (hierarchical TS-FS model) is found or a time limit is reached. The proposed hierarchical TS-FS is evaluated using some well known benchmark applications namely identification of nonlinear systems, prediction of the Mackey-Glass chaotic time-series and some classification problems. When compared to other neural networks and fuzzy systems, the developed hierarchical TS-FS exhibits competing results with high accuracy and smaller size of hierarchical architecture.