1. PART 10 Pattern Recognition 1. Fuzzy clustering 2. Fuzzy pattern recognition 3. Fuzzy image processing FUZZY SETS AND FUZZY LOGIC Theory and Applications

2. Fuzzy clustering Fuzzy c-means clustering method 2

3. Fuzzy clustering 3

4. 4

5. Fuzzy c-means algorithm 5

6. Fuzzy clustering 6

7. 7

8. 8

9. 9

10. Clustering by Equivalence The fuzzy clustering problem can be viewed as the problem of identifying an appropriate fuzzy equivalence relation on given data. It usually cannot be done directly, we can readily determine a fuzzy compatibility relation (reflexive and symmetric) in terms of an appropriate distance function applied to given data. Then, a meaningful fuzzy equivalence relation is defined as the transitive closure of this fuzzy compatibility relation. 10

11. Fuzzy clustering Distance function 11

12. Fuzzy clustering Theorem 10.1 12

13. Fuzzy clustering Example 10.2 13

14. Fuzzy clustering 14

15. Fuzzy clustering 15

16. Fuzzy clustering 16

17. Fuzzy clustering 17

18. Fuzzy clustering Example 10.3 18

19. Fuzzy clustering 19

20. Fuzzy clustering 20

21. Fuzzy clustering 21

22. Fuzzy clustering 22

23. Fuzzy clustering Membership-Roster method 23

24. Fuzzy clustering Example 10.4 24

25. Fuzzy clustering 25

26. Fuzzy clustering 26

27. Fuzzy clustering 27

28. Fuzzy clustering 28

29. Fuzzy clustering Fuzzy syntactic method 29

30. Fuzzy clustering Grammar 30

31. Fuzzy clustering Fuzzy Grammar 31

32. Fuzzy clustering Example 10.5 32

33. Fuzzy clustering 33

34. Fuzzy clustering 34

35. Fuzzy clustering 35

36. Fuzzy clustering 36

37. Fuzzy clustering 37

38. Fuzzy clustering 38

39. Fuzzy image processing Fuzzy matrix 39

40. Fuzzy image processing Example 10.6 40

41. Fuzzy image processing 41

42. Fuzzy image processing 42

43. Fuzzy image processing 43

44. Fuzzy image processing 44

45. Fuzzy image processing 45

46. 46 Exercises 10.2 10.5