Defuzzification
Type Reduction Defuzzification: Karnik-Mendel algorithm for interval type-2 fuzzy sets
Karnik, N.N., Mendel, J.M. · 2001
Strengths
- •Handles full FOU uncertainty
- •Produces an uncertainty interval [c_L,c_R]
- •Proven convergence
Limitations
- •Requires discretisation (N evaluations per FN)
- •Two separate KM runs needed
- •More complex than T1 defuzzification
Method assistant
Grounded explanations: it explains the method, it does not compute.
Assumptions to verify
- •LMF(x) ≤ UMF(x) for all x
- •N_disc ≥ 20 for reliable convergence
When not to use
- •T1 TFN/TrFN inputs: use DEFUZZ-CENTROID
- •IFN/PFN inputs: use DEFUZZ-SCORE-IFN
How to cite
Karnik, N.N.; Mendel, J.M. (2001). Centroid of a type-2 fuzzy set. Information Sciences. https://doi.org/10.1016/S0020-0255(01)00069-X