Supervised training algorithms for B-Spline neural networks and neuro-fuzzy systems

Complete supervised training algorithms for B-Spline neural networks and fuzzy rule-based systems are discussed. By introducing the relationships between B-Spline neural networks and Mamdani (satisfying certain assumptions) and Takagi-Kang-Sugeno fuzzy models, training algorithms developed initially for neural networks can be adapted to fuzzy systems. The standard training criterion is reformulated, by separating its linear and nonlinear parameters. By employing this reformulated criterion with the Levenberg-Marquardt algorithm, a new training method, offering a fast rate of convergence is obtained. It is also shown that the standard Error-Back Propagation algorithm, the most common training method for this class of systems, exhibits a very poor and unreliable performance.