Intelligent hybrid-learning mechanism for IT2 TSK NSFLS2 composed by REFIL-BP methods

The 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. This hybrid-learning algorithm changes the interval type-2 model parameters adaptively to minimize some criteria 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.