Learning fuzzy control rules by a constrained Powell´s method

Learning of fuzzy control rules can be considered as solving a constrained nonlinear optimization problem, in which the objective function is not differentiable. In this case, the problem can be solved by the combination of direct search method and penalty function method. However, it is difficult to know how much a candidate satisfies the constraints. We propose /spl alpha/ level comparison which compares the candidates based on the satisfaction level of constraints. We propose /spl alpha/ constrained method which converts constrained problems to unconstrained problems using /spl alpha/ level comparison. We also propose /spl alpha/ constrained Powell\´s method by applying /spl alpha/ constrained method to Powell\´s direct search method. Through some examples and the learning of fuzzy control rules, we show that the feasible solution can be obtained easily by our method with confirming the satisfaction level. We also show that the evaluation count of the objective function can be decreased by using "lazy evaluation".