A note on the assessment of a fuzzy derivatives’ time-series predictor

This note presents the validation of a new methodology for the prediction of complex discrete-time systems or time-series based on a disturbed fuzzy system. This is a generalisation of the traditional fuzzy system that can incorporate in their linguistic fuzzy relationships of the series and is combined with the ODE Taylor method. Disturbed fuzzy systems are capable of approximating regular functions, as well as their derivatives up to a given order, on compact domains. This results into a new algorithm to solve forecasting problems. The validation of this new time-series forecasting model is done in this brief article using two iconic examples, the Box-Jenkins furnace and a nonlinear dynamic system. The application of the algorithm to both examples, and also a comparative study with other fuzzy and neural network predictors, permits us to conclude that this approach can offer competitive performance. Its virtue lies in the fact that efficiency in accurate and robust forecasting cannot rest solely on a good algorithm but instead should capture and make explicit use of the derivatives of the time-series.

I. Introduction

Work in time-series fuzzy system (FS) modelling concentrates on forecasting future developments of the time-series from values of x up to the current time, x_k. A time-series is a discrete sequence of measured quantities , of some physical system (taken at regular intervals of time) or from human activity data [1].