Abstract
This study uses fuzzy clustering technique to develop a predictive model for interval time series. The proposed model is divided into three phases, with improvements built for each phase. First, overlap distance is used to evaluate the similarity of elements in a universal set of normalized variable data series. The overlap distance is then used to divide the universal set into clusters with an appropriate number. Second, the fuzzy relationship between each element and the clusters is determined based on the fuzzy cluster analysis technique. Third, a new rule is created to interpolate the historical data and forecast the future. The proposed model is detailed for each step and demonstrated using a numerical example. Furthermore, this study theoretically demonstrates convergence. Finally, a MATLAB procedure is created for the proposed model which can be easily implemented for practical applications. Several benchmark data series are used to demonstrate practical applications and show the advantages of the proposed model compared to other models.
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The datasets analyzed during this study are openly available from the public data in the website, and given specifically in the article.
References
Abbasov AM, Mamedova MH (2003) Application of fuzzy time series to population forecasting. In: Proceedings of the 8th symposion on information technology in urban and spatial planning (ITUSP 2003). Vienna University of Technology, pp 545–552
Abreu PH, Silva DC, Moreira JM, Reis LP, Garganta J (2013) Using multivariate adaptive regression splines in the construction of simulated soccer team’s behavior models. Int J Comput Intell Syst 6(5):893–910
Aladag CH, Basaran MA, Egrioglu E, Yolcu U, Uslu VR (2009) Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations. Expert Syst Appl 36(3):4228–4231
Aladag S, Aladag CH, Mentes T, Egrioglu E (2012) A new seasonal fuzzy time series method base on the multiplicative neuron model and SARIMA. Hacettepe J Math Stat 41(3):337–345
Alyousifi Y, Othman M, Husin A, Rathnayake U (2021) A new hybrid fuzzy time series model with an application to predict PM10 concentration. Ecotoxicol Environ Saf 227:112875
Bas E, Egrioglu E, Kolemen E (2022) Training simple recurrent deep artificial neural network for forecasting using particle swarm optimization. Granul Comput 7:411–420
Chen SM (1996) Forecasting enrollments based on fuzzy time series. Fuzzy Sets Syst 81(3):311–319
Chen SM, Hsu CC (2004) A new method to forecast enrollments using fuzzy time series. Int J Appl Sci 2(3):234–244
Chen SM, Jian WS (2017) Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups, similarity measures and PSO techniques. Inf Sci 391–392:65–79
Chen SM, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowl Based Syst 118:204–216
Chen SM, Wang NY (2010) Fuzzy forecasting based on fuzzy-trend logical relationship groups. EEE Trans Syst Man Cybern B Cybern 40(5):1343–1358
Chen SM, Zou XY, Gunawan GC (2019) Fuzzy time series forecasting based on proportions of intervals and particle swarm optimization techniques. Inf Sci 500:127–139
De Carvalho M, Martos G (2022) Modeling interval trendlines: symbolic singular spectrum analysis for interval time series. Int J Forecast 41(1):167–180
De Carvalho FAT, Simões EC (2017) Fuzzy clustering of interval-valued data with City-block and Hausdorff distances. Neurocomputing 266:659–673
De Souza LC, de Souza RMCR, do Amaral GJA (2020) Dynamic clustering of interval data based on hybrid \(L_q\) distance. Knowl Inf Syst 62(2):687–718
Dinh TP, Dan N, Tai V (2022) Improving the ANFIS forecating model for time series based on the fuzzy cluster analysis algorithm. Int J Fuzzy Syst Appl 11(1):1–20
Egrioglu E, Bas E, Aladag CH, Yolcu U (2016) Probabilistic fuzzy time series method based on artificial neural network. Am J Intell Syst 6(2):42–47
Egrioglu E, Fildes R, Baş E (2022) Recurrent fuzzy time series functions approaches for forecasting. Granul Comput 7:163–170
Garg B, Garg R (2016) Enhanced accuracy of fuzzy time series model using ordered weighted aggregation. Appl Soft Comput 48:265–280
Ghosh H, Chowdhury S, Prajneshu (2016) An improved fuzzy time-series method of forecasting based on L-R fuzzy sets and its application. J Appl Stat 43(6):1128–1139
Goyal G, Bisht DCS (2022) Adaptive hybrid fuzzy time series forecasting technique based on particle swarm optimization. Granul Comput 8:373–390
Huarng K (2001) Heuristic models of fuzzy time series for forecasting. Fuzzy Sets Syst 123(3):369–386
Khashe M, Bijari M, Hejazi SR (2011) An extended fuzzy artificial neural networks model for time series forecasting. Iran J Fuzzy Syst 8(3):45–66
Lethikim N, Lehoang T, Vovan T (2021) Automatic clustering algorithm for interval data based on overlap distance. Commun Stat B Simul Comput. https://doi.org/10.1080/03610918.2021.1900248
Lin W, Rivera GG (2016) Interval-valued time series models: Estimation based on order statistics exploring the agriculture marketing service data. Comput Stat Data Anal 100:694–711
Maia ALS, de Carvalho FAT, Ludermir TB (2008) Forecasting models for interval-valued time series. Neurocomputing 7(1):16–18
Mailagaha Kumbure M, Luukka P (2022) A generalized fuzzy k-nearest neighbor regression model based on Minkowski distance. Granul Comput 7:657–671
Ngoc HC, Huynh LN, Thihong DN, Van TV (2022) Building the forecasting model for time series based on the improved fuzzy relationship for variation of data. Int J Comput Intell Appl 21(4):2250026
Pant M, Kumar S (2022) Particle swarm optimization and intuitionistic fuzzy set-based novel method for fuzzy time series forecasting. Granul Comput 7:285–303
Pant M, Kumar S (2022) Fuzzy time series forecasting based on hesitant fuzzy sets, particle swarm optimization and support vector machine-based hybrid method. Granul Comput 7:861–879
Phamtoan D, Vovan T (2020) Automatic fuzzy genetic algorithm in clustering for images based on the extracted intervals. Multimed Tools Appl 80:35193–35215
Phamtoan D, Vovan T (2022) The fuzzy cluster analysis for interval value using genetic algorithm and its application in image recognition. Comput Stat. https://doi.org/10.1007/s00180-022-01215-6
Phamtoan D, Nguyenhuu K, Vovan T (2022) Fuzzy clustering algorithm for outlier-interval data based on the robust exponent distance. Appl Intell 52:6276–6291
Rodrigues PMM, Salish N (2015) Modeling and forecasting interval time series with threshold models. Adv Data Anal Classif 9:41–57
Singh SR (2007) A simple method of forecasting based on fuzzy time series. Appl Math Comput 186(1):330–339
Singh SR (2008) A computational method of forecasting based on fuzzy time series. Math Comput Simul 79(3):539–554
Singh P (2018) Rainfall and financial forecasting using fuzzy time series and neural networks based model. Int J Mach Learn Cybern 9:491–506
Teoh HJ, Cheng CH, Chu HH, Chen JS (2008) Fuzzy time series model based on probabilistic approach and rough set rule induction for empirical research in stock markets. Data Knowl Eng 67(1):103–117
Vovan T (2019) An improved fuzzy time series forecasting model using variations of data. Fuzzy Optim Decis Mak 18:151–173
Vovan T, Ledai N (2019) A new fuzzy time series model based on cluster analysis problem. Int J Fuzzy Syst 21:852–864
Vovan T, Nguyenhuynh L, Lethithu T (2021) A forecasting model for time series based on improvements from fuzzy clustering problem. Ann Oper Res 312:473–493
Yusuf SM, Mohammad A, Hamisu AA (2017) A novel two-factor high order fuzzy time series with applications to temperature and futures exchange forecasting. Niger J Technol 36(4):1124–1134
Zeng S, Chen SM, Teng MO (2019) Fuzzy forecasting based on linear combinations of independent variables, subtractive clustering algorithm and artificial bee colony algorithm. Inf Sci 484:350–366
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This research is funded by Ministry of Education and Training in Vietnam under grant number B2023-TCT-06.
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Vovan, T. Building the forecasting model for interval time series based on the fuzzy clustering technique. Granul. Comput. 8, 1341–1357 (2023). https://doi.org/10.1007/s41066-023-00373-2
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DOI: https://doi.org/10.1007/s41066-023-00373-2