Defuzzification

Defuzzification is the process of producing a quantifiable result in Crisp logic, given fuzzy sets and corresponding membership degrees. It is the process that maps a fuzzy set to a crisp set. It is typically needed in fuzzy control systems.

1. Defuzzification Course : Computational Intelligence Engineering (Soft Computing) Prof. (Dr.) Pravat Kumar Rout Department of EEE, ITER, Siksha ‘O’ Anusandhan (Deemed to be University), Bhubaneswar, Odisha, India 1

2. Fuzzy rule based systems evaluate linguistic if-then rules using fuzzification , inference and composition procedures. They produce fuzzy results which usually have to be converted into crisp output. To transform the fuzzy results in to crisp, defuzzification is performed. Defuzzification is the process of converting a fuzzified output into a single crisp value with respect to a fuzzy set. The defuzzified value in FLC (Fuzzy Logic Controller) represents the action to be taken in controlling the process. 2 Defuzzification Methods

3. 3 What is defuzzification ?

4. 4 Why Defuzzification ?

5. 5 Why Defuzzification ?

6. 6 Why Defuzzification ?

7. Output of a Fuzzy System 7

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12. Different Defuzzification Methods The following are the known methods of defuzzification . Center of Sums Method (COS) Center of gravity (COG) / Centroid of Area (COA) Method Center of Area / Bisector of Area Method (BOA) Weighted Average Method Maxima Methods o First of Maxima Method (FOM) o Last of Maxima Method (LOM) o Mean of Maxima Method (MOM) 12

13. Center of Sums (COS) Method 13

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16. 16 X1 = (0+5)/2 = 2.5 X2 = (3+7)/2 = 5 X3 = (5+8)/2 = 6.5 e.g. Half of the sum of x coordinates

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19. Center of gravity (COG) / Centroid of Area (COA) Method This method provides a crisp value based on the center of gravity of the fuzzy set. The total area of the membership function distribution used to represent the combined control action is divided into a number of sub-areas. The area and the center of gravity or centroid of each sub-area is calculated and then the summation of all these sub-areas is taken to find the defuzzified value for a discrete fuzzy set. 19

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31. Center of Area / Bisector of Area Method (BOA) 31

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33. Weighted Average Method This method is valid for fuzzy sets with symmetrical output membership functions and produces results very close to the COA method. This method is less computationally intensive. Each membership function is weighted by its maximum membership value. The defuzzified value is defined as : 33

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37. Maxima Methods This method considers values with maximum membership. There are different maxima methods with different conflict resolution strategies for multiple maxima. o First of Maxima Method (FOM) o Last of Maxima Method (LOM) o Mean of Maxima Method (MOM) 37

38. First of Maxima Method (FOM) 38

39. Last of Maxima Method (LOM) 39

40. Mean of Maxima Method (MOM) 40

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44. Exercise-1 44

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