1. Richard E. Haskell Oakland University Rochester, MI USA
Fuzzy Logic
Richard E. Haskell
Oakland University
Rochester, MI USA

2. Fuzzy Logic

3. Normal “Crisp” logic where everything must be either True or False leads to
PARADOXES

4. The sentence on the other side
of the line is false
The sentence on the other side
of the line is false

5. A barber has a sign that reads:
“I shave everyone who does
not shave himself”
Who shaves the barber?

6. Fuzzy Logic Lotfi Zadeh - Fuzzy Sets - 1965 Membership functions
Degree of membership between 0 and 1
Fuzzy logic operations on fuzzy sets A and B
NOT A => 1 - A
A AND B => MIN(A,B)
A OR B => MAX (A,B)

7. Membership Functions
Young
Not Young
Age

8. Membership Functions
Not Old
Old
Age

9. Membership Functions Not Old Not Young Age
Middle Age = Not Old AND Not Young
Age

10. Probabiltiy vs. Fuzziness
Probability describes the uncertainty of an event occurrence.
Fuzziness describes event ambiguity.
Whether an event occurs is RANDOM.
To what degree it occurs is FUZZY.

11. Probability:
There is a 50% chance of an apple
being in the refrigerator.
Fuzzy: There is a half an apple in the refrigerator.

12. Fuzzy logic acknowledges and exploits the tolerance for uncertainty and imprecision.

13. Fuzzy Rules IF A AND B THEN L * *
Fuzzy Control
Inputs
Map to Fuzzy Sets
get_inputs();
Fuzzy Rules IF A AND B THEN L * *
fire_rules();
Defuzzification
find_output();
Output

14. Algorithm for a fuzzy controller
do_forever {
get_inputs();
fire_rules();
find_output(); }

15. get_inputs();
Given inputs x1 and x2, find the weight values associated with each input membership function. NM NS Z PS PM
0.7
0.2 X1
W = [0, 0, 0.2, 0.7, 0]

16. Fuzzy Inference fire_rules(); find_output();
Rule 1: If x1 is A1 and x2 is B1 then y is L1
find_output();
Rule 2: If x1 is A2 and x2 is B2 then y is L2
Given: x1 is a and x2 is b
What is y?