DEVELOPMENT OF A FUZZIFIED-TREND MAPPING AND IDENTIFICATION (FTMI) MODEL FOR FUZZY TIME SERIES FORECASTING

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Department of Engineering

ABSTRACT
Fuzzy time series (FTS) forecasting is a technique based on time series and fuzzy logic theory developed for the purpose of analysis and prediction of time series events. The proposed Fuzzified Trend Mapping and Identification (FTMI) model uses a Re-Partitioning Discretization (RPD) approach to optimize the partitioning of the interval lengths and high-order fuzzy relations to construct the trend values. In the proposed model, the mapped out trends are fuzzified into classes both in linguistic and numeric terms to capture both the uncertainty and fuzziness inherent in the trends. Each trend class is given distinct ordinal position for ease of identification during deffuzzification and forecasting. The proposed model is tested on three time series data of different structural and statistical characteristics using mean average percentage error (MAPE) as statistical performance measure. The adaptability of the proposed model to different time series events is also tested using statistical measure of dispersion (variance). Empirical result shows an increase of over 50% in forecast accuracy over pioneer and recent models. Also, the statistical variance of the forecast errors of the proposed model from the MAPE were 0.12, 0.488 and 1.267 compared to 0.58, 8.037 and 4.915 of Shah’s (2012) model for the three time series data respectively. These results demonstrate both the superiority of the proposed FTMI model in accuracy of prediction and its robustness in adaptation to time series of different structural and statistical characteristics when compared to existing models. The effect of increasing the order of difference on both the data trend and the accuracy of forecast are also investigated. Results obtained show that it does not necessarily increase the forecast accuracy regardless of the structure of the time series. The FTMI model is also applied to forecast the short term Internet traffic data of ABU, Zaria. The empirical result shows a MAPE of 0.27 for the Internet traffic, indicating a good accuracy of prediction considering the large size of these traffics.