Determining interval lengths for fuzzy time series forecasting model based on index of fuzzy sets by combining hedge algebra and particle swarm optimization
172 viewsDOI:
https://doi.org/10.54939/1859-1043.j.mst.FEE.2023.271-282Keywords:
Enrolments; Fuzzy time series; FRGs; Hedge algebras; PSO.Abstract
Researchers frequently use fuzzy time series (FTS) forecasting models to estimate future values since they do not rely on the same rigid assumptions as traditional forecasting techniques. There are generally four factors that determine the performance of the FTS forecasting model (1) determining the length of intervals in the universe of discourse, (2) fuzzification rules or feature representation of crisp time series, (3) establishing fuzzy relation groups (FRGs) and (4) creating defuzzification rule to get crisp forecasted value. Considering the first factor and the fourth factor, we propose the hybrid FTS forecasting model combining particle swarm optimization (PSO) and hedge algebra (HA) to improve forecasting accuracy. Where the hedge algebra is utilized as a tool for partitioning the universe of discourse into intervals of different lengths. Then, the times series data are fuzzified into fuzzy sets, the fuzzy relationship groups are established and forecasting output value based on the index of fuzzy sets is calculated. Ultimately, the suggested model collaborates with PSO to obtain the optimal intervals determined by HA. To test the proposed model, we conduct a simulated study on two widely used real-time series and compare the performance with some recently developed models. Error statistics, such as MSE and RMSE show that the proposed model performs better than the comparing models.
References
[1]. Song et al., “Fuzzy time series and its models”, Fuzzy Sets and Systems", 54 (3), 269-277, (1993). DOI: https://doi.org/10.1016/0165-0114(93)90372-O
[2]. Q. Song, B.S. Chissom, “Forecasting Enrollments with Fuzzy Time Series – Part I”, Fuzzy set and systems, vol. 54, pp.1-9, (1993). DOI: https://doi.org/10.1016/0165-0114(93)90355-L
[3]. Zadeh, L. A. “Fuzzy sets”. Information systems, 8, 338–353, (1965). DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[4]. S.M. Chen, “Forecasting Enrollments based on Fuzzy Time Series”, Fuzzy set and systems, vol. 81, pp. 311-319, (1996). DOI: https://doi.org/10.1016/0165-0114(95)00220-0
[5]. H.K. Yu, “Weighted fuzzy time series models for TAIEX forecasting”, Physica A, 349, pp. 609-624, (2005). DOI: https://doi.org/10.1016/j.physa.2004.11.006
[6]. Vedide Rezan Uslu, et al., “A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations”, Swarm and Evolutionary Computation, 15,pp. 19-26, (2014), http://dx.doi.org/10.1016/j.swevo.2013.10.004.
[7]. Huarng, K., “Effective lengths of intervals to improve forecasting in fuzzy time series”. Fuzzy Sets and Systems, 123, 387–394S, (2001). DOI: https://doi.org/10.1016/S0165-0114(00)00057-9
[8]. M. Chen, “Forecasting Enrollments based on hight-order Fuzzy Time Series”, Int. Journal: Cybernetic and Systems, No.33, pp. 1-16, (2002). DOI: https://doi.org/10.1080/019697202753306479
[9]. Lee, L. W. et al., “Handling forecasting problems based on two-factors high-order fuzzy time series”. IEEE Transactions on Fuzzy Systems, 14, 468–477, (2006). DOI: https://doi.org/10.1109/TFUZZ.2006.876367
[10]. S.M. Chen, K Tanuwijaya, “Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques”, Expert Systems with Applications. 38, 15425–15437, (2011). DOI: https://doi.org/10.1016/j.eswa.2011.06.019
[11]. Chen, S.-M., & Chung, N.-Y, “Forecasting enrollments of students by using fuzzy time series and genetic algorithms”, International Journal of Information and Management Sciences, 17, 1-17, (2006).
[12]. Chen, S.M., Chung, N.Y, “Forecasting enrollments using high-order fuzzy time series and genetic algorithms”. International of Intelligent Systems 21, 485–501, (2006b). DOI: https://doi.org/10.1002/int.20145
[13]. I.H. Kuo, et al., “An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization”, Expert systems with applications, 36, 6108–6117, (2006). DOI: https://doi.org/10.1016/j.eswa.2008.07.043
[14]. Huang, Y. L. et al., “A hybrid forecasting model for enrollments based on aggregated fuzzy time series and particle swarm optimization”. Expert Systems with Applications, 38, 8014–8023, (2011). DOI: https://doi.org/10.1016/j.eswa.2010.12.127
[15]. N. C. Dieu, N. V. Tinh, “Fuzzy time series forecasting based on time-depending fuzzy relationship groups and particle swarm optimization”, In: Proceedings of the 9th National Conference on Fundamental and Applied Information Technology Research(FAIR’9), pp.125-133, (2016).
[16]. Nguyen Duy Hieu, Nguyen Cat Ho, Vu Nhu Lan., “Enrollment forecasting based on linguistic time series,” Journal of Computer Science and Cybernetics, vol. 36( 2), pp. 119–137, (2020). DOI: https://doi.org/10.15625/1813-9663/36/2/14396
[17]. Nguyen Cat Ho, Wechler W., “Hedge algebra: An algebraic approach to structures of sets of linguistic truth values”, Fuzzy Sets and Systems, 35, pp. 281-293, (1990). DOI: https://doi.org/10.1016/0165-0114(90)90002-N
[18]. 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
[19]. Kennedy, J., & Eberhart, R., “Particle swarm optimization”. Proceedings of IEEE International Conference on Neural Network, 1942–1948, (1995).
[20]. Bas E, Uslu V.R., Yolcu U, Egrioglu E., “A modified genetic algorithm for forecasting fuzzy time series”, Appl Intell, 41, 453-463, (2014). DOI: https://doi.org/10.1007/s10489-014-0529-x
[21]. L. Wang, X. Liu, W. Pedrycz., “Effective intervals determined by information granules to improve forecasting in fuzzy time series”. Expert Systems withApplications, vol.40, pp.5673–5679, (2013). DOI: https://doi.org/10.1016/j.eswa.2013.04.026
[22]. Lizhu Wang et al., “Determination of temporal information granules to improve forecasting in fuzzy time series”. Expert Systems with Applications, vol.41, pp.3134–3142, (2014). DOI: https://doi.org/10.1016/j.eswa.2013.10.046
[23]. Wei Lu et al., “Using interval information granules to improve forecasting in fuzzy time series”. International Journal of Approximate Reasoning, vol.57, pp.1–18,(2015). DOI: https://doi.org/10.1016/j.ijar.2014.11.002
[24]. Ya’nan Wang, Yingjie Lei, Xiaoshi Fan, and Yi Wang, “Intuitionistic Fuzzy Time Series Forecasting Model Based on Intuitionistic Fuzzy Reasoning”, vol. 2016, Article ID 5035160 , pp 1-12, (2016). DOI: https://doi.org/10.1155/2016/5035160
[25]. Kittikun Pantachang, Roengchai Tansuchat and Woraphon Yamaka, “Improving the Accuracy of Forecasting Models Using the Modified Model of Single-Valued Neutrosophic Hesitant Fuzzy Time Series”, Axioms, 11 (527), (2022). https://doi.org/10.3390/ axioms11100527. DOI: https://doi.org/10.3390/axioms11100527
[26]. K. Khiabani, S. R. Aghabozorgi, “Adaptive Time-Variant Model Optimization for Fuzzy-Time-Series Forecasting”, IAENG International Journal of Computer Science, 42(2), pp.1-10, (2015).
[27]. Jilani TA, Burney SMA, “Multivariate stochastic fuzzy forecasting models”. Expert Syst Appl, 353, 691–700, (2008). DOI: https://doi.org/10.1016/j.eswa.2007.07.014
[28]. Yusuf SM, Mu’azu MB, Akinsanmi.O, “A Novel Hybrid fuzzy time series Approach with Applications to Enrollments and Car Road Accident”, International Journal of Computer Applications, 129 (2), 37 – 44, (2015). DOI: https://doi.org/10.5120/ijca2015906852
[29]. Shyi-Ming Chen, Xin-Yao Zou, “Gracius Cagar Gunawan, Fuzzy time series forecasting based on proportions of intervals and particle swarm optimization techniques”, Information Sciences 500, 127–139, (2019). DOI: https://doi.org/10.1016/j.ins.2019.05.047
[30]. V.R. Uslu, E. Bas, U. Yolcu, E. Egrioglu, “A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations”, Swarm Evol. Comput. 15, 19–26, (2014). DOI: https://doi.org/10.1016/j.swevo.2013.10.004
