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)

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Presentation transcript:

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)

Definition of a Type-2 Fuzzy Set

Type-2 Membership Function

Definition of Vertical Slice

Gaussian Type-2 Fuzzy Set

Operations on Type-2 Fuzzy Sets

Type Reduction

Interval Type-2 Sets

Operations on Interval Type-2 Sets

Type-1 Fuzzy Inference

Type-2 Fuzzy Inference

1.Jerry M. Mendel, “Type-2 Fuzzy Sets and Systems: An Overview,” IEEE Computational Intelligence Magazine, February 2007, pp 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 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 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 Nilesh N. Karnik, and Jerry M. Mendel, “Operations on Type-2 Fuzzy Sets,” Fuzzy Sets and Systems, Vol. 122, 2001, pp References AUC library)