On the Monotonicity of Smooth Fuzzy Systems

This article addresses the monotonicity property of the smooth fuzzy systems (SFSs). We have derived the sufficient conditions for the monotonicity of SFS and could show that, since the smooth fuzzy compositions are differentiable to the membership functions (MFs), irrespective to the shape of the membership function, one can obtain the monotonic SFS by the proper selection of the inference scheme and the consequent parts. This gives more flexibility that the MFs can have discontinuity in the universe of discourse or switch their values and the SFS still keep to be monotonic. This property is useful for the control and modeling of switched and hybrid dynamic systems.