This slide presents about Fuzzy If - Then Rule.

1. Fuzzy Rules and Fuzzy Implications
Course: Computational Intelligence Engineering (Soft Computing)
Prof. (Dr.) Pravat Kumar Rout
Department of EEE, ITER,
Siksha ‘O’Anusandhan (Deemed to be University),
Bhubaneswar, Odisha, India
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2. What is Fuzzy Rule?
 A fuzzy rule can be defined as a conditional statement in the form:
IF x is A
THEN y is B
where x and y are linguistic variables; and A and B are linguistic values
determined by fuzzy sets on the universe of discourses X and Y, respectively.
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3. What is Fuzzy Rule?
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4. What is the difference between classical and fuzzy rules?
 A classical IF-THEN rule uses binary logic, for
 Rule: 1
IF speed is > 100
THEN
Min_stopping_Dist = 300
 Rule: 2
IF speed is < 40
THEN
Max_stopping_distance = 40
 The variable speed can have any numerical value between 0 and 220 km/h,
and stopping_distance can take either value 300 or 40. In other words,
classical rules are expressed in the black-and-white language of Boolean
logic.
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5. Continue....
 We can also represent the stopping distance rules in a fuzzy form:
 Rule1
IF speed is fast
THEN
stopping_distance is long
 Rule: 2
IF speed is slow
THEN
stopping_distance is short
 In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse)
between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast.
The universe of discourse of the linguistic variable stopping distance can be between 0 and
300 m and may include such fuzzy sets as short, medium and long.
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6. 6 Fuzzy Implication: Example-1

7. 7 Fuzzy Implications: Example-2

8. 8 Fuzzy Implication: Example-2

9. Interpretation of fuzzy rules
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10. Interpretation as A coupled with B 1/3
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11. Interpretation as A coupled with B 2/3
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12. Interpretation as A coupled with B 3/3
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13. Product Operators
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14. 14 Interpretation of A entails B 1/3

15. 15 Interpretation of A entails B 2/3

16. Interpretation of A entails B 3/3
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Example 3: Zadeh’s Max-Min rule 1/6

18. 18 Example 3: Zadeh’s Max-Min rule 2/6

19. Example 3: Zadeh’s Max-Min rule: 3/6
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20. 20 Example-3: 4/6

21. Example-3 5/6
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22. 22 Example-3: 6/6

23. Example-4 ½
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24. Example-4 2/2
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25. Interpretation of Fuzzy Implications
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35. Fuzzy controller parts: Four Major Parts
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36. Rules formation
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37. Aggregation of the propositions and the
implications of the fuzzy rule base
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38. 38 Continue…

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