Handling higher order time series forecasting approach in intuitionistic fuzzy environment

Abstract

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].

KEYWORDS:

• Fuzzy time series
• intuitionistic fuzzy number
• membership grades
• accuracy function
• higher order IFLR

Acknowledgements

The authors are very thankful to the editor and the anonymous reviewers for their constructive comments and suggestions that greatly helped to improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Abhishekh

Abhishekh received his M.Sc. (Mathematics) degree from the Banaras Hindu University (Varanasi-India) in 2012. Currently, he is a research scholar in the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India. His research areas are mainly fuzzy optimisation, intuitionistic fuzzy set, and FTS forecasting.

Sanjay Kumar

Sanjay Kumar received B.Sc. and M.Sc. degrees in Mathematics from Magadh University, Bodh-Gaya, Bihar in 1990 and 1993, respectively. He was a part-time research scholar in the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India. He is currently a Joint Registrar (Development and Administration) at the Banaras Hindu University, India. His research interests include soft computing techniques and the forecasting of FTS models.