a short and complete presentation on fuzzy logic.

1. FUZZY LOGIC Presented by: Anu Gupta (CSE/08/48) Jyoti Jain (CSE/08/67) Kritika Kedia (CSE/08/53) Neha Gupta (CSE/08/69) Ritu Bafna (CSE/08/68) 1

3. What is fuzzy logic?

4. Fuzzy Vs Crisp Set

5. Membership Functions

6. Fuzzy Logic Vs Probability

7. Why use Fuzzy Logic?

8. Fuzzy Linguistic Variables

9. Operations on Fuzzy Set

10. Fuzzy Applications

11. Case Study

12. Drawbacks

13. Conclusion

14. Bibliography2

16. Jan Lukasiewicz proposed three-valued logic : True, False and Possible

17. Finally Lofti Zadeh published his paper on fuzzy logic-a part of set theory that operated over the range [0.0-1.0]3

19. Fuzzy logic is multivalued. It deals with degrees of membership and degrees of truth.

20. Fuzzy logic uses the continuum of logical values between 0 (completely false) and 1 (completely true).Boolean (crisp) Fuzzy 4

21. For example, let a 100 ml glass contain 30 ml of water. Then we may consider two concepts: Empty and Full. In boolean logic there are two options for answer i.e. either the glass is half full or glass is half empty. 100 ml 30 ml In fuzzy concept one might define the glass as being 0.7 empty and 0.3 full. 5

24. a

25. a

26. b

27. bFuzzy set Crisp set a: member of crisp set A b: not a member of set A a: full member of fuzzy set A’ b: not a member of set A’ c:partial member of set A’ 7

28. Crisp set Fuzzy Vs. Crisp Set Fuzzy set 8

30. Support: region characterized by nonzero membership in set A’ i.e. μ(x) >0.

31. Boundary: region characterized by partial membership in set A’ i.e. 0< μ (x) <1core 1 0 x boundary support 9

32. Membership Functions adult(x)= { 0, if age(x) < 16years (age(x)-16years)/4, if 16years < = age(x)< = 20years, 1, if age(x) > 20years } 10

34. In terms of probability, the natural language statement would be ”there is an 80% chance that Jane is old.”

35. While the fuzzy terminology corresponds to “Jane’s degree of membership within the set of old people is 0.80.’

36. Fuzzy logic uses truth degrees as a mathematical model of the vagueness phenomenon while probability is a mathematical model of ignorance.11

38. Fuzzy logic is conceptually easy to understand.

39. Fuzzy logic is tolerant of imprecise data.

40. Fuzzy logic is based on natural language.12

42. Temp:{Freezing, Cool, Warm, Hot}13

43. Operations on Fuzzy Set Consider: A= {1/2 + .5/3 + .3/4 + .2/5} B= {.5/2 + .7/3 + .2/4 + .4/5} μA μB B A >Fuzzy set (A) >Fuzzy set (B) >Resulting operation of fuzzy sets 14

44. INTERSECTION (A ^ B) UNION (A v B) COMPLEMENT (¬A) μA U μA ∩ B μA ‘ μA∩ B= min (μA(x), μB(x)) {.5/2 + .5/3 + .2/4 + .2/5} μA’= 1-μA(x) {1/1 + 0/2 + .5/3 + .7/4 + .8/5} μAUB= max (μA(x), μB(x)) {1/2 + .7/3 + .3/4 + .4/5} 15

46. 25 % Cloud Cover ?16

47. Input: Cover: {Sunny, Partly cloudy, Overcast} Temp: {Freezing, Cool, Warm, Hot} Output: Speed: {Slow, Fast} 17

50. 25% Cover Sunny = 0.8, Cloudy = 0.219

51. Calculating: If it's Sunny and Warm, drive Fast Sunny(Cover)Warm(Temp)Fast(Speed) 0.8  0.7 = 0.7 Fast = 0.7 If it's Cloudy and Cool, drive Slow Cloudy(Cover)Cool(Temp)Slow(Speed) 0.2  0.4 = 0.2 Slow = 0.2 20

53. Find centroids: Location where membership is 100%

54. Speed = weighted mean = (2*25+7*75)/(9) = 63.8 mph 21

56. Cameras : for auto-focus

57. Home appliances: Rice cookers , Dishwashers , Washing machines and others 22

61. http://www.seattlerobotics.org/encoder/mar98/fuz/flindex.html

62. http://en.wikipedia.org/wiki/Fuzzy_logic

63. http://www.dementia.org/~julied/logic/index.html

64. http://mathematica.ludibunda.ch/fuzzy-logic.html25