Learning fuzzy control rules by vector simplex method

The learning of fuzzy control rules can be considered as a nonlinear optimization problem in which the objective function isn´t differentiable. Also, the problem is usually defined as a multi-objective optimization problem (MOP) because of plural control targets. Since the objective function in a MOP is vector-valued, their set is a partially ordered set. Thus, in MOPs, a complete optimal solution, which minimizes all objectives simultaneously, does not necessarily exist. Pareto optimality is the representative concept of optimality in MOPs. When using Pareto-optimal solutions, it is very important for the decision maker (DM) to obtain the set of all Pareto-optimal solutions and to select one solution based on his global preference information. In this paper, we propose a multi-objective optimization method caalled the vector simplex method, which can obtain the approximate set of Pareto-optimal solutions directly and quickly. Also, we learn fuzzy control rules for an inverted pendulum by using the vector simplex method, and we show that this method is effective enough to learn fuzzy control rules in comparison with other optimization methods