Fuzzy Time Series Forecasting Model based on Centre of Gravity Similarity Measure

Abstract

This paper proposes a new method for measuring fuzzy forecasting accuracy (FFA) based on centre of gravity (COG) similarity measure approach. Fuzzy time series (FTS) data represented in trapezoidal fuzzy numbers (TrFNs) form, average based length partitioning method, and first order fuzzy logical relation are used in developing the FTS forecasting model. The COG similarity measure is calculated between the fuzzified historical data and fuzzy forecasted values. The distance of COG similarity measure represents the error of the forecasting model which is the uniqueness of the FFA method. The proposed forecasting model is applied in a numerical example of unemployment rate with the forecasting error of 0.0241 obtained. The new FFA can be directly obtained from the fuzzy forecasted values without going through the defuzzification process as compared to other fuzzy forecasting models. The historical data and forecasted values remained in the TrFNs form and, thus, this proposed forecasting model preserved the information that has been kept during the forecasting procedure from being lost. The proposed model can be applied in other time series data such as forecasts on finance, tourism and weather.