Remark on Membership Functions in Neuro-Fuzzy Systems

Abstract

The sigmoidal membership function applied in the neuro-fuzzy systems with hierarchical input domain partition and gradient tuning method may deteriorate the tuning process. The function’s high value plateau with very low derivative’s value stops the gradient based tuning procedure. This leads to less adequate models and poorer results elaborated by the system. In such systems the membership function should satisfy the condition that the low values of derivatives in respect of the function parameters should be followed by the low values of membership function itself. The points of the domain that do not fulfil this condition may only be isolated point of the domain. The function should have no high membership plateaux. The functions suitable for systems with hierarchical input domain partition are bell-like functions as Gaussian, generalised bell function, (a)symmetric π function.