Fuzzy Time Series Forecasting Models Evaluation Based on A Novel Distance Measure
Pp. 1-23 (23)
Cagdas Hakan Aladag and I. Burhan Turksen
In the literature, many models based on fuzzy systems have been utilized to
solve various real world problems from different application areas. One of this areas is
time series forecasting. Successful forecasting results have been obtained from fuzzy
time series forecasting models in many studies. To determine the best fuzzy time series
model among possible forecasting models is a vital decision. In order to evaluate fuzzy
time series forecasting models, conventional performance measures such as root mean
square error or mean absolute percentage error have been widely utilized in the
literature. However, the nature of fuzzy logic is not taking into consideration when
such conventional criteria are employed since these criteria are computed over crisp
values. When fuzzy time series forecasting models are evaluated, using criteria which
work based on fuzzy logic characteristics is wiser. Therefore, Aladag and Turksen 
suggested a new performance measure which is calculated based on membership values
to evaluate fuzzy systems. It is called as membership value based performance
measure. In this study, a novel distance measure is firstly defined and a new
membership value based performance measure based on this new distance measure is
proposed. The proposed criterion is also applied to real world time series in order to
show the applicability of the suggested measure.
Forecasting, Fuzzy time series, Membership value based performance
measure, Membership values, Model evaluation, Performance criterion, Real
world time serie.
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada.