Monotonic Takagi–Sugeno models with cubic spline membership functions

Abstract

In the paper we present sufficient monotonicity conditions for zero order Takagi–Sugeno fuzzy systems with cubic spline membership functions. Those fuzzy models have some advantages comparing with commonly used membership functions. In contrast to triangular membership functions the corresponding mapping is smooth. Comparing to Gaussian membership functions the monotonicity conditions are less conservative, more intuitive and admit membership functions with different width. Finally, the derived monotonicity conditions are formulated as linear constraints on the parameters of fuzzy system that can be easily incorporated into related optimization problems solvable by efficient algorithms. Performance of the proposed fuzzy system is tested on two benchmark datasets and output prediction of a nonlinear dynamical system.