Defuzzification

This presentation discusses about the Defuzzification process under Fuzzy logic

1. Dr . C.V. Suresh Babu Professor Department of IT Hindustan Institute of Science & Technology DEFUZZIFICATION

2. Action Plan Defuzzification Why defuzzification ? Defuzzification applications Defuzzification process Lambda-cut method Defuzzification methods Quiz at the end of session`

3. FUZZY LOGIC CRISP LOGIC In fuzzy logic we can take intermediate value between 0 and 1 Elements are allowed to be partially included in set Used in Fuzzy Controllers. It has infinite value It can deal with representation of human intelligence. Test Yourself

4. FUZZY LOGIC CRISP LOGIC In fuzzy logic we can take intermediate value between 0 and 1 in crisp logic we can take binary value either 0 or 1 (True or False). Elements are allowed to be partially included in set Elements is either the member of a set or not Used in Fuzzy Controllers. Used in Digital Design. It has infinite value It has Bi-valued. It can deal with representation of human intelligence. It can’t deal with representation of human intelligence. Answers

5. DEFUZZIFICATION Defuzzification means the fuzzy to crisp conversion . Defuzzification is a mapping process from a space of fuzzy control actions defined over an output universe of discourse into a space of crisp ( nonfuzzy ) control actions. Defuzzification is a process of converting output fuzzy variable into a unique number. Defuzzification process has the capability to reduce a fuzzy set into a crisp single-valued quantity or into a crisp set; to convert a fuzzy matrix into a crisp matrix; or to convert a fuzzy number into a crisp number . 5

6. Why defuzzification ? The fuzzy results generated can not be used in an application, where decision has to be taken only on crisp values.

7. Defuzzification applications In many practical applications, a control command is given as a crisp value. a process to get a non-fuzzy control action that best represents the possibility distribution of an inferred fuzzy control action. no systematic procedure for choosing a good defuzzification strategy , select one in considering the properties of application case

8. Defuzzification process Defuzzification is the process of conversion of fuzzy quantity into a precise quantity . [ A] first part of fuzzy output (C1) [B] Second part of fuzzy output (C2) [C] Union of part [A] and [B]. The union of two membership function in values the max operator, which is going to be the outer envelope of the two or more shapes

9. Lambda-cut method Lmabda -cut method is applicable to derive crisp value of a fuzzy set or relation . Thus Lambda-cut method for fuzzy set Lambda-cut method for fuzzy relation In many literature, Lambda-cut method is also alternatively termed as Alpha-cut method.

10. Lamda -cut method for fuzzy set In this method a fuzzy set A is transformed into a crisp set A for a given value of In other-words, That is, the value of Lambda-cut set A is x, when the membership value corresponding to x is greater than or equal to the specified . This Lambda-cut set A is also called alpha-cut set .

11. Defuzzification methods include: [ 1] max membership principle. [2] centroid method. [3] weighted average method. [4] mean max membership. [5] center of sums. [6] centre of largest area. [7] first of maxima, last of maxima.

12. [1] Max – membership principle: M   c  ( x* ) >  M   c  ( x ) for all x ∈ X

13. [2] Centroid method centre of mall, centre of gravity or area. X A = ∫ M s ( x ). x.dx ∫ M c ( x ). dx

14. [3] Weighted average method Valid for symmetrical output membership function. Each membership function is weighted by its max membership value.

15. [4] Mean max membership method: This is known as middle of the maxima.

16. 5] Centre of sums: Algebraic sum of individual fuzzy the union, here, interesting areas are value twice, the defuzzified value X +

17. [6] Centre of largest area When output consists of at least two converse fuzzy subsets which are not overlapping. When o/p fuzzy set has at least two converse regions, then the centre of gravity of converse fuzzy sub region having the largest area is used to obtain defuzzified value.

18. [7] first of maxima (last of maxima) This method uses the overall output or union of all individual output fuzzy sets ci for determining the smallest value of the domain maximized membership in ci

19. Test Yourself Fuzzy logic is : a) Used to respond to questions in a humanlike way b) A new programming language used to program animation c) The result of fuzzy thinking d) A term that indicates logical values greater than one 2. Which of the following is not a part of fuzzy logic Systems Architecture? A. Fuzzification Module B. Knowledge Base C. Defuzzification Module D. Interference base 3. The 7 Defuzzification methods are:

20. Answers Fuzzy logic is : a) Used to respond to questions in a humanlike way b) A new programming language used to program animation c) The result of fuzzy thinking d) A term that indicates logical values greater than one 2. Which of the following is not a part of fuzzy logic Systems Architecture? A. Fuzzification Module B. Knowledge Base C. Defuzzification Module D. Interference base 3. The 7 Defuzzification methods are: [ 1] max membership principle. [2] centroid method. [3] weighted average method. [4] mean max membership. [5] center of sums. [6] centre of largest area. [7] first of maxima, last of maxima.