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Meaning of “fuzzy”, Definition of Fuzzy Logic

Fuzzy Logic. Introduction. Meaning of “fuzzy”, Definition of Fuzzy Logic. C overed with fuzz; Of or resembling fuzz; N ot clear; indistinct A fuzzy recollection of past events. N ot coherent; confused A fuzzy plan of action.

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Meaning of “fuzzy”, Definition of Fuzzy Logic

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  1. Fuzzy Logic Introduction Meaning of “fuzzy”, Definition of Fuzzy Logic • 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. • Fuzzy logic: a form of knowledge representation suitable for notions that cannot be defined precisely, but depend upon their contexts,it deals with reasoning that is approximate rather than fixed and exact.

  2. Fuzzy Logic Introduction Origins of Fuzzy Logic • The earliest record can be traced back as far as to the ancient Greece period • LotfiZadeh(1965)  The first to publish ideas of fuzzy logic • ToshireTerano(1972)  The first to organize a working group of fuzzy system • F. L. Smidth et. al.  The first to market fuzzy expert system

  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 Control (Single Input) • 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: Heater Fan Control (Two Inputs) • Problem: Change the speed of the fan, based on the room temperature and humidity. • The temperature is classified into four conditions: Cold, Cool, Warm, and Hot. • The humidity can be defined by: Low, Medium, and High. • The available wattage settings of the heater fan are Zero, Low, Medium, and High. Temperature Humidity Fan Wattage

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

  17. 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.

  18. 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.

  19. Fuzzy Logic Fuzzy Logic Control Example: Stopping A Car Fuzzy Membership Functions 25 m  100 % 0 m  0 % 10 m/s  100 % 0 m/s  0 % Negative to emphasize that the value is decreasing

  20. Fuzzy Logic Fuzzy Logic Control Example: Stopping A Car Time Response

  21. Neural Networks Introduction Preparation Assignment • Ensure yourself to install Matlab 7 in your computer, along with Matlab Simulink, Control System Toolbox, and Fuzzy Logic Toolbox. • The Fuzzy Logic Toolbox can be opened by typing “fuzzy” on the command window. • Read the Fuzzy Toolbox Manual that can be found in the directory where Matlab is installed. One version of the manual can be found on the lecture website.

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