Necessity of parametric conditions for monotonic TSK fuzzy systems
Jin-Myung Won, Fakhri Karray · 2012
Input-output monotonicity is an important property found in many physical systems. This paper reviews parametric conditions of monotonic Takagi-Sugeno-Kang (TSK) fuzzy systems, and discusses its sufficiency and necessity. In author's previous work, the sufficiency of the conditions was shown, but the necessity has remained an open question. This study analytically proves that the necessity holds when a single-input TSK fuzzy system employs two rules. For the cases of three rules, counter examples are provided to verify that the necessity of the conditions violates.