On the Continuity of Type-1 and Interval Type-2 Fuzzy Logic Systems

@article{Wu2011OnTC,
  title={On the Continuity of Type-1 and Interval Type-2 Fuzzy Logic Systems},
  author={Dongrui Wu and Jerry M. Mendel},
  journal={IEEE Transactions on Fuzzy Systems},
  year={2011},
  volume={19},
  pages={179-192}
}
This paper studies the continuity of the input-output mappings of fuzzy logic systems (FLSs), including both type-1 (T1) and interval type-2 (IT2) FLSs. We show that a T1 FLS being an universal approximator is equivalent to saying that a T1 FLS has a continuous input-output mapping. We also derive the condition under which a T1 FLS is discontinuous. For IT2 FLSs, we consider six type-reduction and defuzzification methods (the Karnik-Mendel method, the uncertainty bound method, the Wu-Tan method… CONTINUE READING

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