The monotonicity and convexity of unnormalized interval type-2 TSK Fuzzy Logic Systems
Tiechao Wang, Jianqiang Yi, Chengdong Li · 2010
This paper applies prior knowledge - monotonicity and convexity - to a Single-Input-Single-Output (SISO) un-normalized interval type-2 Takagi-Sugeno-Kang (TSK) Fuzzy Logic System (FLS). Sufficient conditions are provided to guarantee its monotonicity and convexity with respect to its input, respectively. The derived monotonic conditions focus on a zeroth-order TSK fuzzy model. Also, the corresponding proofs for the convex conditions of both the zeroth-order and first-order TSK fuzzy models are given, respectively. For the zeroth-order fuzzy systems, simulation examples demonstrate the validity of the theorems.