1. Universe, membership function, variables, operations, relations
Fuzzy Sets
Universe, membership function, variables, operations, relations

2. Zadeh’s Complaint
Clearly, the “class of all real numbers which are much greater than 1,” or “the class of beautiful women,” or “the class of tall men,” do not constitute classes or sets in the usual mathematical sense of these terms (Zadeh, 1965).

3. Weekend Days Is Saturday a weekend day? 1 (yes, or true)
Is Tuesday a weekend day?
0 (no, or false)
Is Friday a weekend day?
0.8 (mostly yes, but not completely)
Is Sunday a weekend day?
0.95 (Yes, but not quite as Saturday)

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

5. Fuzzy Set ‘Positive’
-100
-50 50
100
0.5 1
Universe
Membership

6. Around 4 2 4 6 8
0.5 1
Measurements
Membership

7. Tank Level Control LL LH V1

8. High Level 20 40 60 80
100
0.5 1
Percent full
Membership

9. Examples Of Primary Sets
0.5 1
(a)
(d)
(g)
(j)
(b)
(e)
(h)
(k)
-100
100
(c)
(f)
(i)
(l)

10. Age 20 40 60 80 100 0.5 1 Age Membership old more or less old young20 40 60 80
100
0.5 1
Age
Membership
old
more or less old
young
very young
not very young

11. High And Low Levels 20 40 60 80
100
0.5 1
Percent full
Membership

12. A Term Set
Neg
Zero
Pos 1
0.5
Membership

13. Linguistic Variable DTQUE Neg Zero Pos -3 3 % per h Ling. var.
3 % per h
Ling. var.
Fuzzy var.
Base var.

14. Set Operations 20 40 60 80
100
0.5 1
Membership A B
A U B
A I B

15. Set Operations 20 40 60 80
100
0.5 1
Membership A B
A U B
A I B

16. Fuzzy Relations
Dewey Louie
Huey =
Donald
0.8
0.9
0.5
0.6

17. Computing with words Operations, implication, inference
Fuzzy Logic
Computing with words
Operations, implication, inference

18. Boolean OR

19. Cayley Table

20. Fuzzy OR

21. Cayley Table

22. Modus Ponens

23. To Infer
Reach (an opinion) from facts or reasoning
Conclude something

24. Cayley Table

25. Boolean Implication

26. Implication
When in Rome, do like the Romans

27. To Imply
Suggest (sth) as a logical consequence

28. Gödel Implication

29. Fuzzy Modus Ponens

30. Inference 1. When in Rome, do like the Romans 2. I am in Rome
3. I do like the Romans

31. Generalised Modus Ponens

32. Tank Level Control LL LH V1

33. Two Rules If the level is low, then open V1
If the level is high, then close V1

34. Mamdani Implication

35. Compositional Rule Of Inference

36. Why fuzzy logic?
Easy to understand
Flexible
Tolerant of imprecision

37. Concepts Sets, universe, membership, continuous/discrete, singletons
Linguistic variables, term set, primary term
Fuzzification, defuzzification
Operations, relations, composition
Fuzzy logic, implication, inference