Learning of rule importance for fuzzy controllers to deal with inconsistent rules and for rule elimination

Extraction of correct and precise rules from experts is a difficult problem. Moreover, even when the extracted rules are correct, all of them may not have equal importance to achieve the goal of the fuzzy system. Rule tuning is usually achieved through modification of membership functions. Effect of changing a membership function is global in the sense, it influences all rules that involve the membership function. Here we propose an effective extension of the ordinary fuzzy controller model which incorpotates an importance factor for each rule. The importance factor allows tuning of the system at the rule level. Of course, one can still tune the membership functions. The extended model enables us to cope with incorrect and/or incompatibile rules and thereby enhances the robustness, flexibility and system modeling capability. It also helps us to eliminate redundant rules easily. For the Takagi-Sugeno framework, we derive the learning algorithm for the rule importance factor as well as that for the consequent. We demonstrate the superiority of the extended model through extensive simulation results using the inverted pendulum.