![]() Several simulation examples are provided to demonstrate the accuracy and effectiveness of the affine T-S fuzzy modelling algorithm. Employing conditions 1 and 2 in Definition 39 applied now to affine hyperplanes, we obtain the following expression for such reflections: (1. An affine T-S fuzzy model with compact IF-THEN rules could thus be generated systematically. An affine hyperplane with respect to a root system R is defined by We can also consider reflections r, k about affine hyperplanes. Finally, the gradient descent algorithm is included to adjust the fuzzy model precisely. Additionally, a check and repartition algorithm is suggested to prevent the inappropriate premise structure where separate regions of data shared the same regression model. The antecedent fuzzy sets of each IF-THEN fuzzy rule are acquired by projecting the fuzzy partitions matrix U onto the axes of individual antecedent variable to obtain point-wise defined fuzzy sets and to approximate these point-wise defined fuzzy sets by normal bell-shaped membership functions. Once the number of clusters is determined, the consequent parameters of each IF-THEN rule are directly obtained from the functional cluster representatives (affine linear functions). Keywords: Piecewise affine hybrid systems, polyhedral sets, controllability. Particularly, a novel cluster validity criterion for FCRM is set up to choose the appropriate number of clusters (rules). Each cluster is essentially a basis of the fuzzy rule that describes the system behaviour, and the number of clusters is just the number of fuzzy rules. Firstly, the fuzzy c-regression model (FCRM) clustering technique is applied to partition the product space of the given input–output data into hyper-plan-shaped clusters. An effective approach is developed to establish affine Takagi-Sugeno (T-S) fuzzy model for a given nonlinear system from its input–output data.
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