Generalized defuzzification strategies and their parameter learning procedures

Defuzzification is a procedure of crucial importance for fuzzy systems because a final crisp output (control) action is required in many theoretical and practical applications. The choice of defuzzification strategy, therefore, can directly affect the success of such applications. Among the existing strategies, neither the center of area (COA) nor the mean of maximum (MOM) emerges as the better defuzzification strategy. A compromise strategy that combines the two methods may offer a synergetic solution. In this paper, the authors introduce two new objective defuzzification strategies, Gaussian distribution transformation-based defuzzification (GTD) and polynomial transformation-based defuzzification (PTD), which are based on a discrete universe of discourse. Both strategies can perform better than the existing strategies and the PTD strategy offers a generalized defuzzification tool for a wide class of practical problems. Both strategies include the COA and MOM strategies as special cases, and both are based on parameter learning processes using the extended Kalman filter as their iterative improvement algorithms on sample database containing fuzzy sets and the associate defuzzified values. The proposed parameter learning procedures are capable of either off-line or on-line processing.