Hierarchical fuzzy design by a multi-objective evolutionary hybrid approach

This paper presents a new tree hierarchical representation of type-2 fuzzy systems. The proposed system is called the type-2 hierarchical flexible beta fuzzy system (T2HFBFS) and is trained based on two-phase optimization mechanism. The first optimization step is a multi-objective structural learning phase. This phase is based on the multi-objective extended immune programming algorithm and aims to obtain an improved T2HFBFS structure with good interpretability-accuracy trade-off. The second optimization step is a parameter tuning phase. Using a hybrid evolutionary algorithm, this phase allows the adjustment of antecedent and consequent membership function parameters of the obtained T2HFBFS. By interleaving the two learning steps, an optimal and accurate hierarchical type-2 fuzzy system is derived with the least number of possible rules. The performance of the system is evaluated by conducting case studies for time series prediction problems and high-dimensional classification problems. Results prove that the T2HFBFS could attain superior performance than other existing approaches in terms of achieving high accuracy with a significant rule reduction.