1. Type-2 Fuzzy Sets Slides prepared by: Dr. Ashraf Abdelbar American University in Cairo (using material extracted from various papers by J. Mendel and colleagues)

2. Definition of a Type-2 Fuzzy Set

3. Type-2 Membership Function

4. Definition of Vertical Slice

5. Gaussian Type-2 Fuzzy Set

7. Operations on Type-2 Fuzzy Sets

8. Type Reduction

9. Interval Type-2 Sets

12. Operations on Interval Type-2 Sets

13. Type-1 Fuzzy Inference

14. Type-2 Fuzzy Inference

16. 1.Jerry M. Mendel, “Type-2 Fuzzy Sets and Systems: An Overview,” IEEE Computational Intelligence Magazine, February 2007, pp. 20-29. 2.Jerry M. Mendel, Robert I. Bob John, and Feilong Liu, “Interval Type- 2 Fuzzy Logic Systems Made Simple,” IEEE Transactions on Fuzzy Systems, Vol. 14, No. 6, December 2006, pp. 808-821. 3.Jerry M. Mendel, and Robert I. Bob John, “Type-2 Fuzzy Sets Made Simple,” IEEE Transactions on Fuzzy Systems, Vol. 10, No. 2, April 2002, pp. 117-127. 4.Nilesh N. Karnik, Jerry M. Mendel, and Qilian Lang, “Type-2 Fuzzy Logic Systems,” IEEE Transactions on Fuzzy Systems, Vol. 7, No. 6, December 1999, pp. 643-658. 5.Nilesh N. Karnik, and Jerry M. Mendel, “Operations on Type-2 Fuzzy Sets,” Fuzzy Sets and Systems, Vol. 122, 2001, pp. 327-348. References (avail @ AUC library)