A unifying approach to defuzzification and comparison of the outputs of fuzzy controllers

This paper addresses the defuzzification of the fuzzy set outputs of fuzzy controllers from a comparison or ranking perspective. This is done by emphasizing the fuzzy controller as a decision-making system. Based on the extensive study and justification of the fuzzy-set comparison criteria that were developed and published elsewhere by the author, a ranking and, thus, a defuzzification index is introduced. This index is shown to overcome the disadvantages of the commonly used defuzzification methods whose attempted justifications based on probabilistic arguments have not been successful. In addition, the proposed index is based on the generalization of the Hurwicz criterion that is usually adopted in decision making under nonprobabilistic uncertainty and it encompasses the pessimistic maximin and the optimistic maximax criteria as special cases