Summary

Defuzzification strategy (DS), a mapping from a fuzzy set on a universe of discourse into a designated nonfuzzy (crisp) space, plays an ultimately important role in fuzzy theory and applications because a crisp control action is required in many cases. An example can be found from the driving instruction case given by Bezdek in his editorial for the inaugural issue of IEEE Transactions on Fuzzy Systems [¹]. After the teacher advises the student to “apply the brakes pretty soon,” the student will try to defuzzify, in his way, the fuzzy message from the teacher to act correctly in front of a traffic light. Defuzzification action is usually produced by a decision-making algorithm that selects the best crisp value based on a fuzzy set. Since Zadeh first noticed the lack of systematic defuzzification procedures [²], three commonly used strategies—center of area (COA) or center of gravity (COG), mean of maximum (MOM), and max criterion (MC)—have been developed for fuzzy control applications [³]. Detailed analyses of these strategies by Kiszka et al. [⁴], Kickert and Mamdani [⁵], Braae and Rutherford [⁶], Larkin [⁷], as well as Scharf and Mandic [⁸], concluded that the COA and MOM strategies usually perform better than the MC strategy, but neither the COA nor the MOM strategy has an absolute advantage over the other. Specifically, the COA strategy yields better steady-state performance and a smoother response but is less transient than the MOM strategy.