1. PART 9 Fuzzy Systems 1. Fuzzy controllers 2. Fuzzy systems and NNs 3. Fuzzy neural networks 4. Fuzzy Automata 5. Fuzzy dynamic systems FUZZY SETS AND FUZZY LOGIC Theory and Applications

2. 2 Fuzzy Controllers 2

3. 3 3

4. 4 Five steps of design: Step 1: Select linguistic states for I/O variables 4

5. 5 Fuzzy Controllers Step 2: Define fuzzification functions for input variables 5

6. 6 Fuzzy Controllers Step 3: Formulate fuzzy inference rules 6

7. 7 Fuzzy Controllers Step 4: Making inferences by inference engine Step 5: Define a suitable defuzzification method 7

8. 8 Fuzzy Controllers Center of area method For the discrete case: 8

9. 9 Fuzzy Controllers Center of maxima method 9

10. 10 Fuzzy Controllers Mean of maxima method 10

11. 11 Fuzzy Controllers Mean of maxima method 11

12. 12 Fuzzy Controllers 12

13. 13 Fuzzy Controllers 13

14. 14 Fuzzy Controllers 14

15. 15 Fuzzy Controllers 15

16. 16 Fuzzy Controllers 16

17. 17 Fuzzy Controllers 17

18. 18 Fuzzy systems and NNs 18

19. 19 Fuzzy neural networks 1.Inputs, outputs of different layers, and weights are fuzzy numbers 2. 19

20. 20 Fuzzy neural networks 3. 4.Stopping criteria 5.Fuzzy the BP algorithm 20

21. 21 Fuzzy automata Definition A fuzzy automaton its states are characterized by fuzzy sets, and the production of responses and next states is facilitated by appropriate fuzzy relations. 21

22. 22 Fuzzy automata 22

23. 23 Fuzzy automata 23

24. 24 Fuzzy automata Example : A fuzzy automaton with 24

25. 25 Fuzzy automata 25 internal states at any time t be defined by the vectors

26. 26 Fuzzy automata 26

27. 27 Fuzzy automata

28. 28 Fuzzy dynamic systems General dynamic system 28

29. 29 Fuzzy dynamic systems 29

30. 30 Exercises 9.2 9.4