1. Defuuzification Techniques for Fuzzy Controllers Chun-Fu Kung System Laboratory, Department of Computer Engineering and Science, Yuan-Ze University, Taiwan, Republic of China 2000/7/26 Jean J. Saade and Hassan B. diab

2. Outline zIntroduction zElements of fuzzy controller zCommon defuzzification methods zNew defuzzification technique zConclusion

3. Introduction zAiming at improving the performance of fuzzy controller, several useful concepts and approaches have been developed. zSelf-organizing controllers, artificial neural network, and fuzzy relational equations. zDefuzzification is a procedure for determining the crisp value that is regarded as the most representative of the output fuzzy sets.

4. Introduction (cont.) zThe mean of maxima (MOM) and the center of gravity (COG) methods have been mostly used to come up with crisp controller outputs. zThe min-max weighted average formula (min-max WAF) is another powerful method to compute the crisp values.

5. Fuzzy Controller zA fuzzy controller is formed by input and output fuzzy sets assigned over the controller input and output variables, a collection of inference rules and a defuzzifier. zWe usually using Zadeh’s compositional rule of inference to give an output fuzzy set for each crisp input pair (x 0,y 0 )

6. Common Defuzzification Method zIn order that this output be transformed into a crisp one, three main defuzzification techniques have so far been applied: the MOM, COG and min-max WAF. zCOG method: zMin-max method:

7. Case1 Study

8. New Technique zWe required that the sum of the membership grades of any crisp input value in the different overlapping fuzzy sets defined over an input variable be 1. zInstead of using the minimum operation for AND in order to combine the membership grades of crisp input value in the fuzzy sets, the product of there grade is applied. zCOOL -> s co %, WARM -> s wa % and HOT -> s hp %. zDRY -> s dr %, MOIST -> s mo % and WET -> s we %

9. New Technique (cont.)

11. Result Humidity = 70%, left is Min-Max WAF and right is New method

12. Result (cont.) left is MOM, right is COG

13. Result (cont.) left is Min-Max WAF, right is New method

14. Case2 Study (washing machine) left is MOM, right is COG

15. Case2 Study (cont.) left is Min-Max WAF, right is New method

16. Conclusion zThis technique integrates the defuzzification problem into the global setting of the elements of the fuzzy controller. zThe new technique doesn’t consider probabilistic averaging and helps achieve performance objectives in an easy and systematic manner. zA nonprobabilistic and parametrized defuzzification method is a research project that has almost been completed.

17. Conclusion (cont.) left is Fuzzy Fan, right is Washing Machine (δ=0.5)