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A Robust Interval Type-2 TSK Fuzzy Logic System Design based on Chebyshev Fitting

Nora Boumella, Karim Djouani, and Mohammed Boulemden
International Journal of Control, Automation, and Systems, vol. 10, no. 4, pp.727-736, 2012

Abstract : This paper presents two approaches for the design of an interval Type-2 TSK Fuzzy Logic System (FLS), taking into account the uncertainties about the consequent parameters. While the first approach deals with the tuning of the consequent parameters used for the system output computation, the second one, based on a linear Chebyshev fitting, shows more robustness as it considers the consequent sets instead of only the consequent crisp values. This approach deals with all parameters at the consequent level, by taking into account the upper and lower bounds of the consequent set instead of the mean value. The effectiveness of both approaches in terms of robustness to noise is evaluated through the design of IT2 TSK FLS A1-C1 forecasters for the Mackey-Glass time-series.

Keyword : Chebyshev fitting, generalized orthogonality principle (GOP), interval type-2 fuzzy logic system (IT2 FLS), Takagi-Sugeno-Kang (TSK).

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