Modeling fuzzy time series data using exponential smoothing method

Akbari, Mohammad Ghasem; Zarei, Reza

doi:10.22124/jmm.2026.33373.3059

Modeling fuzzy time series data using exponential smoothing method

Articles in Press

Document Type : Research Article

Authors

Mohammad Ghasem Akbari ¹
Reza Zarei ²

¹ Department of Statistics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Birjand‎, ‎Birjand‎, ‎Iran‎.

² Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

10.22124/jmm.2026.33373.3059

Abstract

This paper proposes a novel approach for modeling and analyzing fuzzy time series data using the exponential smoothing method under imprecise conditions. The proposed model employs weights derived from a decreasing exponential function, parameterized by a smoothing factor \(\lambda\), which assigns greater importance to recent data while gradually diminishing the influence of older observations. Performance is evaluated using three complementary criteria: the Mean Similarity Measure (MSM, higher values indicate better agreement between observed and predicted fuzzy sets), the Root Mean Square Error (RMSE, lower values indicate higher predictive accuracy), and the Mean Absolute Percentage Error (MAPE, lower values indicate better percentage accuracy). On a simulated dataset with trend and outliers, the proposed model achieves MSM \(= 0.569\), RMSE \(= 16.13\), and MAPE \(= 21.5\%\); on real ozone concentration data (1980--2019), MSM \(= 0.531\), RMSE \(= 5.25\) (ppb), and MAPE \(= 6.2\%\); and on a software reliability dataset, MSM \(= 0.591\), RMSE \(= 1.152\), and MAPE \(= 4.6\%\). These results significantly outperform the benchmark methods of Hesamian et al. (2022) and Zarei et al. (2020). The proposed method thus demonstrates improved accuracy and robustness for fuzzy time series forecasting.

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