2. Meaning of “fuzzy”, Definition of Fuzzy Logic
Introduction
Meaning of “fuzzy”, Definition of Fuzzy Logic
Covered with fuzz;
Of or resembling fuzz;
Not clear; indistinct A fuzzy recollection of past events.
Not coherent; confused A fuzzy plan of action.
Unclear, blurred, or distorted Some 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.

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

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

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

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

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

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

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

10. Some Definitions Support of a fuzzy set A
Fuzzy Logic
Set Definition
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} x
(x) 1
Alpha cuts usual for implementation in a computer
α = 0.6

11. 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

12. Fuzzy Logic
Fuzzy Logic Operators
Logic Operators

13. Boolean OR and Fuzzy OR Boolean OR Fuzzy OR Fuzzy Logic
Fuzzy Logic Operators
Boolean OR and Fuzzy OR
Boolean OR
Fuzzy OR

14. Boolean AND and Fuzzy AND
Fuzzy Logic
Fuzzy Logic Operators
Boolean AND and Fuzzy AND
Boolean AND
Fuzzy AND

15. Example: Air Fan Control (Single Input)
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.

16. Example: Heater Fan Control (Two Inputs)
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.
Humidity
Temperature
Fan Wattage

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

18. Example: Stopping A Car
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.

19. Example: Stopping A Car
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.

20. Example: Stopping A Car
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

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

22. Preparation Assignment
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.