TSK fuzzy model with minimal parameters

•An efficient genetic algorithm (GA) to generate a simple and well defined.•TSK model is proposed.•Three different attributes characterizing the structure of a TSK model, are optimized simultaneously (MSE, number of rules and number of parameters).•Simulation results show that our approach outperforms some methods proposed in previous work.

In this paper, an efficient genetic algorithm (GA) to generate a simple and well defined TSK model is proposed. The approach is derived from the use of the improved Strength Pareto Evolutionary Algorithm (SPEA-2), where the genes of the chromosome are arranged into control genes and parameter genes. These genes are in a hierarchical form so that the control genes can manipulate the parameter genes in a more effective manner. In our approach, we first apply the back-propagation algorithm to optimize the parameters of the model (parameters of membership functions and fuzzy rules), then we apply the SPEA-2 to optimize the number of fuzzy rules, the number of parameters and to fine tune these parameters.Two well-known dynamic benchmarks are used to evaluate the performance of the proposed algorithm. Simulation results show that our modeling approach outperforms some methods proposed in previous work.

Graphical abstractOptimization of TSK fuzzy model using SPEA2 with hierarchical chromosomes.Figure optionsDownload full-size imageDownload as PowerPoint slide