Hybrid learning mechanism for interval A2-C1 type-2 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic systems

A proposed learning methodology based on a hybrid mechanism for training interval A2-C1 type-2 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic systems uses a recursive square-root filter to tune the type-1 consequent parameters and the steepest descent method to tune the interval type-2 antecedent parameters. The proposed hybrid-learning algorithm changes the interval type-2 model parameters adaptively to minimize some criterion function as new information becomes available and to match desired input-output data pairs. Its antecedent sets are type-2 fuzzy sets, its consequent sets are type-1 fuzzy sets, and its inputs are interval type-2 non-singleton fuzzy numbers with uncertain standard deviations. As reported in the literature, the performance indices of hybrid models have proved to be better than those of the individual training mechanisms used alone. Comparison with non-hybrid interval A2-C1 type-2 Takagi-Sugeno-Kang fuzzy logic systems and with non-hybrid A1-C0 type-1 Takagi-Sugeno-Kang fuzzy logic systems shows that the proposed hybrid mechanism is a well-performing non-linear adaptive method that enables the interval type-2 fuzzy model to match an unknown non-linear mapping and to converge very fast. Experiments were carried out involving the application of the hybrid interval A2-C1 type-2 non-singleton type-2 Takagi-Sugeno-Kang fuzzy logic systems for modeling and prediction of the scale-breaker entry temperature in a hot strip mill for three different types of coils. The results demonstrate how the interval type-2 fuzzy system learns from selected input-output data pairs and improves its performance as hybrid training progresses.