Meaning of “fuzzy”

2. Fuzzy Logic Introduction Meaning of “fuzzy” • Covered with fuzz; • Of or resembling fuzz; • Not clear; indistinctA fuzzy recollection of past events. • Not coherent; confusedA fuzzy plan of action. • Unclear, blurred, or distortedSome fuzzy pictures from a Russian radar probe.

3. Fuzzy Logic Introduction Spring Summer Autumn Winter 1 Membership 0.5 0 Time of the year 4 Seasons

4. Fuzzy Logic Introduction Tall Persons 1 : A person is tall 0 : A person is not tall

5. Fuzzy Logic Introduction Room Temperature 1 : room is warm 0 : room is not warm Incorporation of human’s perception

6. Fuzzy Logic Set Definition A=“young” 1 0 Classical Sets young = { x  P | age(x) ≤20 } Characteristic function:

7. Fuzzy Logic Set Definition A=“young” A=“young” 1 1 0 0 Fuzzy Sets Classical Logic Fuzzy Logic Element x belongs to set A with a certain “degree of membership”: (x)[0,1] Element x whether belongs to set A or not at all: (x){0,1}

8. Fuzzy Logic Set Definition A=“young” 1 0 Fuzzy Sets Definition: Fuzzy Set A = {(x,A(x)) | xX, A(x)  [0,1]}is defined by a universe of discourse x where0 ≤x≤ 100 and a membership function A where A(x)  [0,1]

9. Fuzzy Logic Set Definition (x) 1 0 x Some Definitions • Support of a fuzzy set A • supp(A) = { x X | A(x) > 0 } • Core of a fuzzy set A • core(A) = { xX |A(x) = 1 } • α-cut of a fuzzy set A • Aα= { xX |A(x)  α} α= 0.6

10. Fuzzy Logic Fuzzy Logic Control Fuzzy Logic Control (FLC) • Fuzzy Logic Control (FLC) may be viewed as a branch of intelligent control which serves as an emulator of human decision-making behaviour which is approximate rather than exact. • FLC uses the IF-THEN rules, similar to binary control (Programmable Logic Controller, PLC). • Rule Format: • Ri: IF x is Aj AND y is Bk THEN z is Cl • Ri: IF x is Aj OR y is Bk THEN z is Cl

11. Fuzzy Logic Fuzzy Logic Operators Logic Operators

12. Fuzzy Logic Fuzzy Logic Operators Boolean OR and Fuzzy OR Boolean OR Fuzzy OR

13. Fuzzy Logic Fuzzy Logic Operators Boolean AND and Fuzzy AND Boolean AND Fuzzy AND

14. Fuzzy Logic Fuzzy Logic Control Example: Air Fan • Conventional (On-Off) Control: • IF temperature > X °C, THEN run fan, • ELSE stop fan. • Fuzzy Control: • IF temperature is hot, THEN run fan at full speed; • IF temperature is warm, THEN run fan at moderate speed; • IF temperature is comfortable, THEN maintain fan speed; • IF temperature is cool, THEN slow fan; • IF temperature is cold, THEN stop fan.

15. Fuzzy Logic Fuzzy Logic Control Example: Stopping A Car Break force Mass of the car Initial position Initial velocity

16. Fuzzy Logic Fuzzy Logic Control Example: Stopping A Car P-Control PD-Control With Kp = –240, the car will stop at the traffic light after 10 s. Choosing ζ = 1, Td = 1, Kp = 6000, the car will stop at the traffic light after 5 s.

17. Fuzzy Logic Fuzzy Logic Control Example: Stopping A Car • Fuzzy Logic Control: • IF distance is long AND approach is fast, THEN brake zero; • IF distance is long AND approach is slow, THEN brake zero; • IF distance is short AND approach is fast, THEN brake hard; • IF distance is short AND approach is slow, THEN brake zero.

18. Fuzzy Logic Fuzzy Logic Control Fuzzy Membership Functions

19. Fuzzy Logic Fuzzy Logic Control Response