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Defuuzification Techniques for Fuzzy Controllers

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

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Defuuzification Techniques for Fuzzy Controllers

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

  2. Outline • Introduction • Elements of fuzzy controller • Common defuzzification methods • New defuzzification technique • Conclusion

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

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

  5. Fuzzy Controller • A 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. • We usually using Zadeh’s compositional rule of inference to give an output fuzzy set for each crisp input pair (x0,y0)

  6. Common Defuzzification Method • In 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. • COG method: • Min-max method:

  7. Case1 Study

  8. New Technique • We 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. • Instead 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. • COOL -> sco%, WARM -> swa% and HOT -> shp%. • DRY -> sdr%, MOIST -> smo% and WET -> swe%

  9. New Technique (cont.)

  10. 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 • This technique integrates the defuzzification problem into the global setting of the elements of the fuzzy controller. • The new technique doesn’t consider probabilistic averaging and helps achieve performance objectives in an easy and systematic manner. • A 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)

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