Handling higher order time series forecasting approach in intuitionistic fuzzy environment

This study presents a new method of forecasting based on a higher order intuitionistic fuzzy time series (FTS) by transforming FTS data into intuitionistic FTS data via defining their appropriate membership and non-membership grades. The fuzzification of time series data is intuitionistic fuzzification which is based on the maximum score degree of intuitionistic fuzzy numbers. Also, the intuitionistic fuzzy logical relationship groups are defined and introduced into a defuzzification process for a higher order intuitionistic FTS that enhances in the forecasted output. In order to assess the performance of the proposed method, the method has been implemented on the historical data of rice production. The comparison result shows that the proposed method can achieve a better forecasting accuracy rate in terms of RMSE and MAPE than the existing methods such as Song and Chissom [(1993). Forecasting enrolments with fuzzy time series - Part I. Fuzzy Sets and System, 54, 1-9], Chen [(1996). Forecasting enrolments based on fuzzy time series. Fuzzy Sets and System, 81, 311-319], Singh [(2007a). A simple method of forecasting based on fuzzy time series. Applied Mathematics and Computation, 186, 330-339] and Abhishekh, Gautam, and Singh [(2017). A refined weighted method for forecasting based on type 2 fuzzy time series. International Journal of Modelling and Simulation, 38, 180-188; (2018). A score function based method of forecasting using intuitionistic fuzzy time series. New Mathematics and Natural Computation, 14(1), 91-111].