Monotonic Smooth Takagi–Sugeno Fuzzy Systems With Fuzzy Sets With Compact Support

In this paper, sufficient conditions on monotonicity of Takagi-Sugeno (T-S) fuzzy systems with linear consequent parts with smooth membership functions with compact support (i.e., equal to zero outside a compact set) are derived. The presented conditions considerably reduce conservatism of those known for T-S fuzzy systems utilizing membership functions with the support that is not compact. Besides, two illustrative examples will demonstrate that the monotonicity requirement imposed on fuzzy systems may significantly improve their extrapolation capability.