An enhanced fuzzy time series forecasting model using Gaussian membership functions and PSO-based parameter optimization
DOI:
https://doi.org/10.54939/1859-1043.j.mst.CSCE9.2025.23-34Keywords:
Fuzzy time series; Fuzzy logical relationship groups; Gaussian functions; PSO; Enrollments; Ron95.Abstract
In the context of data-driven decision making and increasing market volatility, accurate time series forecasting plays a crucial role in sectors such as education and energy. This paper presents a novel fuzzy time series (FTS) model that integrates Gaussian membership functions with Particle Swarm Optimization (PSO) to simultaneously optimize the universe of discourse ( , ) and the standard deviations of Gaussian functions. The key innovation lies in the combination of dynamic fuzzification with PSO-based parameter optimization, effectively addressing the limitations of static partitioning and manual tuning in traditional FTS models. Furthermore, the model employs time-dependent fuzzy logical relationship groups (TD-FLRGs) to improve forecasting accuracy in handling non-linear and uncertain data. The proposed model is evaluated on the Alabama university enrollment dataset (1971–1992) and validated using Vietnam's RON95 gasoline prices. With seven intervals and first-order relationships, it achieves a Root Mean Squared Error (RMSE) of 318.7. These results highlight the model's superior performance and demonstrate its potential as a scalable and adaptable solution for real-time forecasting in dynamic environments.
References
[1]. G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, “Time Series Analysis: Forecasting and Control”, Holden-Day, (1970).
[2]. D. C. Montgomery, E. A. Peck, and G. G. Vining, “Introduction to Linear Regression Analysis”, Wiley, (2012).
[3]. C. C. Holt, “Forecasting seasonals and trends by exponentially weighted moving averages”, Office of Naval Research Memorandum, no. 52, (1957).
[4]. S. Makridakis et al., “Forecasting: Methods and Applications”, Wiley, (1998).
[5]. Q. Song and B. S. Chissom, “Forecasting enrollments with fuzzy time series — Part I”, Fuzzy Sets and Systems, vol. 54, no. 1, pp. 1–9, (1993). DOI: https://doi.org/10.1016/0165-0114(93)90355-L
[6]. Q. Song and B. S. Chissom, “Fuzzy time series and its models”, Fuzzy Sets and Systems, vol. 54, no. 3, pp. 269–277, (1993). DOI: https://doi.org/10.1016/0165-0114(93)90372-O
[7]. S. J. Taylor and B. Letham, “Forecasting at scale”, The American Statistician, vol. 72, no. 1, pp. 37–45, (2018). DOI: https://doi.org/10.1080/00031305.2017.1380080
[8]. S. M. Chen, “Forecasting enrollments based on fuzzy time series”, Fuzzy Sets and Systems, vol. 81, no. 3, pp. 311–319, (1996). DOI: https://doi.org/10.1016/0165-0114(95)00220-0
[9]. K. Huarng, “Effective lengths of intervals to improve forecasting in fuzzy time series”, Fuzzy Sets and Systems, vol. 123, no. 3, pp. 387–394, (2001). DOI: https://doi.org/10.1016/S0165-0114(00)00057-9
[10]. S. R. Singh, “A simple method of forecasting based on fuzzy time series”, Applied Mathematics and Computation, vol. 186, no. 1, pp. 330–339, (2007). DOI: https://doi.org/10.1016/j.amc.2006.07.128
[11]. E. Egrioglu et al., “A new approach based on the optimization of the length of intervals in fuzzy time series”, Journal of Intelligent & Fuzzy Systems, vol. 21, no. 6, pp. 365–374, (2010).
[12]. H. Kuo et al., “An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization”, Expert Systems with Applications, vol. 36, no. 3, pp. 6108–6117, (2009). DOI: https://doi.org/10.1016/j.eswa.2008.07.043
[13]. Y. L. Huang et al., “An improved forecasting model based on the weighted fuzzy time series”, Soft Computing, vol. 15, no. 7, pp. 1335–1347, (2011).
[14]. L. W. Lee, L. H. Wang, and S. M. Chen, “Temperature prediction and TAIFEX forecasting based on high-order fuzzy logical relationships and genetic algorithms”, Expert Systems with Applications, vol. 33, no. 4, pp. 923–934, (2007). DOI: https://doi.org/10.1016/j.eswa.2006.05.015
[15]. C. H. H. Cheng, J. R. R. Chang, and C. A. A. Yeh, “Entropy-based and trapezoid fuzzification-based fuzzy time series approaches for forecasting IT project cost”, Technological Forecasting and Social Change, vol. 73, no. 5, pp. 524–542, (2006). DOI: https://doi.org/10.1016/j.techfore.2005.07.004
[16]. S. Askari and N. Montazerin, “A high-order multivariable fuzzy time series forecasting algorithm based on fuzzy clustering”, Expert Systems with Applications, vol. 42, no. 4, pp. 2121–2135, (2015). DOI: https://doi.org/10.1016/j.eswa.2014.09.036
[17]. M. Chen, “Forecasting enrollments based on high-order fuzzy time series”, Cybernetics and Systems, vol. 33, pp. 1–16, (2002). DOI: https://doi.org/10.1080/019697202753306479
[18]. H. K. Yu, “Weighted fuzzy time series models for TAIEX forecasting”, Physica A: Statistical Mechanics and its Applications, vol. 349, nos. 3–4, pp. 609–624, (2005).
[19]. L. Wang et al., “Effective intervals determined by information granules to improve forecasting in fuzzy time series”, Expert Systems with Applications, vol. 40, no. 14, pp. 5673–5679, (2013). DOI: https://doi.org/10.1016/j.eswa.2013.04.026
[20]. E. Egrioglu, “A new approach based on artificial neural networks for high-order multivariate fuzzy time series”, Expert Systems with Applications, vol. 36, no. 7, pp. 10589–10594, (2009). DOI: https://doi.org/10.1016/j.eswa.2009.02.057
[21]. M. Bose and K. M. Mali, “A novel data partitioning and rule selection technique for modelling high-order fuzzy time series”, Applied Soft Computing, (2017). DOI: https://doi.org/10.1016/j.asoc.2017.11.011
[22]. N. V. Tinh, “Enhanced forecasting accuracy of fuzzy time series model based on combined fuzzy C-mean clustering with particle swarm optimization”, International Journal of Computational Intelligence Applications, vol. 19, p. 2050017, (2020). DOI: https://doi.org/10.1142/S1469026820500170
[23]. J. Kennedy and R. Eberhart, “Particle swarm optimization”, Proceedings of the International Conference on Neural Networks, vol. 4, pp. 1942–1948, (1995).
[24]. N. D. Hieu, N. C. Ho, and V. L. Lan, “Enrollment forecasting based on linguistic time series”, Journal of Computer Science and Cybernetics, vol. 36, no. 2, pp. 119–137, (2020). DOI: https://doi.org/10.15625/1813-9663/36/2/14396
[25]. L. Wang et al., “Determination of temporal information granules to improve forecasting in fuzzy time series”, Expert Systems with Applications, vol. 41, pp. 3134–3142, (2015). DOI: https://doi.org/10.1016/j.eswa.2013.10.046
[26]. M. Pant and S. Kumar, “Fuzzy time series forecasting based on hesitant fuzzy sets, particle swarm optimization and support vector machine-based hybrid method”, Granular Computing, vol. 7, pp. 761–789, (2022). DOI: https://doi.org/10.1007/s41066-021-00300-3
[27]. S. S. Gautam, A. Abhishekh, and S. R. Singh, “A modified weighted method of time series forecasting in intuitionistic fuzzy environment”, Opsearch, vol. 57, no. 3, pp. 1022–1041, (2020). DOI: https://doi.org/10.1007/s12597-020-00455-8
[28]. K. Bisht, D. K. Joshi, and S. Kumar, “Dual hesitant fuzzy set-based intuitionistic fuzzy time series forecasting”, Ambient Communications and Computer Systems, pp. 317–329, (2018). DOI: https://doi.org/10.1007/978-981-10-7386-1_28
[29]. P. D. Phong, “A time series forecasting model based on linguistic forecasting rules”, Journal of Computer Science and Cybernetics, vol. 37, no. 1, pp. 23–42, (2021). DOI: https://doi.org/10.15625/1813-9663/37/1/15852
[30]. K. Pantachang et al., “Improving the accuracy of forecasting models using the modified model of single-valued neutrosophic hesitant fuzzy time series”, Axioms, vol. 11, p. 527, (2022). DOI: https://doi.org/10.3390/axioms11100527
[31]. V. R. Uslu et al., “A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations”, Swarm and Evolutionary Computation, vol. 15, pp. 19–26, (2014). DOI: https://doi.org/10.1016/j.swevo.2013.10.004
[32]. S. M. Chen and N. Y. Chung, “Forecasting enrollments of students by using fuzzy time series and genetic algorithms”, International Journal of Information and Management Sciences, vol. 17, pp. 1–17, (2006).
[33]. S. Lubna et al., “An improved fuzzy time series forecasting model based on hesitant fuzzy sets”, Journal of Fuzzy Extension and Applications, vol. 5, no. 2, pp. 173–189, (2024).
[34]. S. M. Chen and N. Y. Chung, “Forecasting enrolments using high-order fuzzy time series and genetic algorithms”, International Journal of Intelligent Systems, vol. 21, pp. 485–501, (2006). DOI: https://doi.org/10.1002/int.20145
[35]. W. R. Qiu, X. D. Liu, and H. L. Li, “A generalized method for forecasting based on fuzzy time series”, Expert Systems with Applications, vol. 38, no. 8, pp. 10446–10453, (2011). DOI: https://doi.org/10.1016/j.eswa.2011.02.096
[36]. J. Wang and K. Chen, “Frequency-weighted fuzzy time series model based on time variations”, Classics in Applied Mathematics, vol. 11, no. 2, pp. 76–90, (2013).
[37]. W. Qiu, C. Zhang, and Z. Ping, “Generalized fuzzy time series forecasting model enhanced with particle swarm optimization”, International Journal of u- and e-Service, Science and Technology, vol. 8, no. 7, pp. 129–140, (2015). DOI: https://doi.org/10.14257/ijunesst.2015.8.5.11
