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Journals / Nevşehir Hacı Bektaş Veli Üniversitesi SBE Dergisi / 2026 / Cilt: 15 Sayı: 1

An innovative hybrid approach to forecasting İnterval Time Series data with Elman Artificial Neural Networks and a modified adaptive Network-Based Fuzzy Inference System

Elman Yapay Sinir Ağları ve Modifiye Adaptif Ağ Bulanık Çıkarım Sistemi kullanan yeni bir Hibrit Zaman Serisi Tahmin Yaklaşımı

Ebrucan İslamoğlu(Nevşehir Hacı Bektaş Veli Üniversitesi)0000-0002-8297-7370
Murat Alper Başaran(Alanya Alaaddin Keykubat University)0000-0001-9887-5531
Pages
223–247
Publication Date
2025-03-27
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In conclusion, comparisons have been provided to show the effectiveness of the recommended model.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Interval valued Time Series (ITS) techniques have been employed to conduct both modeling and forecasting in the data analysis.
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Key Findings & Data:This manuscript recommends a hybrid model that combines two operative methods, which are the Modified Adaptive Network Based Fuzzy Inference System (MANFIS) and Elman Artificial Neural Network (ERNN) model, to be employed for ITS to generate a forecast.
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Conclusion & Impact:In conclusion, comparisons have been provided to show the effectiveness of the recommended model.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:aralık değerli zaman serisi · modifiye ANFIS · ERNN

Abstract

Interval valued Time Series (ITS) techniques have been employed to conduct both modeling and forecasting in the data analysis. This manuscript recommends a hybrid model that combines two operative methods, which are the Modified Adaptive Network Based Fuzzy Inference System (MANFIS) and Elman Artificial Neural Network (ERNN) model, to be employed for ITS to generate a forecast. The ITS mainly differs from conventional (non-interval) time series by taking into account both highs and lows of interval simultaneously. By doing so, possible interrelations between bounds can be taken into account. The recommended hybrid strategy takes into account this aspect of the data to forecasting interval time series data combining both ERNN and MANFIS. The recommended method composes of two parts. The initial part constructs the algorithm pertaining to the ANFIS structure. The second part is based on the ERNN model structure. The advantages of the proposed method can be expressed as in 1. The recommended method, called ERNN-MANFIS, uses the optimization method of particle swarm optimization to train the model, 2. Addressing both linear and nonlinear aspects of forecasting, this approach offers dual advantages, known respectively as model-based and data-based approaches. It is trained by using fuzzy c-means method and particle swarm optimization. In the fuzzification step of the input values, membership values are systematically obtained by using fuzzy c-means clustering technique. By doing this, the prediction performance of the method is improved. Seven different real datasets are used to affirm the effectiveness of the mentioned approach. In addition, the results were compared with the results of previous models available in the literature. In conclusion, comparisons have been provided to show the effectiveness of the recommended model.

Özet

Aralık Değerli Zaman Serisi (ITS) teknikleri, veri analizinde hem modelleme hem de tahmin yapmak için kullanılmaktadır. Bu makale, ITS için tahmin üretmek amacıyla iki etkili yöntemi birleştiren hibrit bir model önermektedir: Modifiye Adaptif Ağ Tabanlı Bulanık Çıkarım Sistemi (MANFIS) ve Elman Yapay Sinir Ağı (ERNN) modeli. ITS, geleneksel (aralık olmayan) zaman serilerinden, aralığın hem en yüksek hem de en düşük değerlerini aynı anda dikkate alarak farklılık gösterir. Bu şekilde, sınırlar arasındaki olası ilişkiler dikkate alınabilir. Önerilen hibrit strateji, ERNN ve MANFIS'i birleştirerek veri aralığı zaman serisi verilerini tahmin etmeye yönelik bu yönü dikkate alır. Önerilen yöntem iki kısımdan oluşmaktadır. İlk kısım, ANFIS yapısına ait algoritmayı oluşturur. İkinci kısım ise ERNN model yapısına dayanır. Önerilen yöntemin avantajları şu şekilde ifade edilebilir: 1. ERNN-MANFIS olarak adlandırılan önerilen yöntem, modeli eğitmek için parçacık sürü optimizasyonu yöntemini kullanır, 2. Hem doğrusal hem de doğrusal olmayan tahmin yönlerini ele alarak, sırasıyla model tabanlı ve veri tabanlı yaklaşımlar olarak bilinen iki avantaj sunar. Bu yöntem, bulanık c-means yöntemi ve parçacık sürü optimizasyonu kullanılarak eğitilmektedir. Girdi değerlerinin bulanıklaştırma adımında, üyelik değerleri sistematik olarak bulanık c-means kümeleme tekniği kullanılarak elde edilir. Bu şekilde, yöntemin tahmin performansı artırılır. Belirtilen yaklaşımın etkinliğini doğrulamak için yedi farklı gerçek veri seti kullanılmıştır. Ayrıca, sonuçlar literatürde mevcut olan önceki modellerin sonuçları ile karşılaştırılmıştır. Sonuç olarak, önerilen modelin etkinliğini göstermek için karşılaştırmalar sağlanmıştır.

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Cite This Article

İslamoğlu, E., Başaran, M. A. (2025). An innovative hybrid approach to forecasting İnterval Time Series data with Elman Artificial Neural Networks and a modified adaptive Network-Based Fuzzy Inference System. Nevşehir Hacı Bektaş Veli Üniversitesi SBE Dergisi, Cilt: 15 Sayı: 1, 223–247. https://doi.org/10.30783/nevsosbilen.1508663

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References (78)

  1. Bock, H. H., & Diday, E. (2000). Analysis of symbolic data: Explanatory methods for extracting statistical information from complex data. Springer Science & Business Media.
  2. Maia, A. L. S., & De Carvalho, F. A. (2011). Holt's exponential smoothing and neural network models for forecasting interval-valued time series. International Journal of Forecasting, 27(3), 740–759.
  3. https://doi.org/10.1016/j.ijforecast.2010.02.012.
  4. Liu, Y.-J., Zhang, W.-G., & Zhang, P. (2013). A multi-period portfolio selection optimization model by using interval analysis. Economic Modelling, 33, 113–119. https://doi.org/10.1016/j.econmod.2013.03.006
  5. Erol, E., Çağdaş, H. A., Ufuk, Y., & Eren, B. (2014). A new adaptive network-based fuzzy inference system for time series forecasting. Aloy Journal of Soft Computing and Applications, 2(1), 25–32.
  6. Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. Proceedings of the IEEE International Conference on Neural Networks, 4, 1942–1948.
  7. Jang, J. S. R. (1992). Self-learning fuzzy controller based on temporal back-propagation. IEEE Transactions on Neural Networks, 3(5), 714–723.
  8. Jin, X. (2013). ANFIS model for time series prediction. Applied Mechanics and Materials, 385-386, 1411–1414.
  9. Song, Q., & Chisom, B. S. (1993b). Forecasting enrollments with fuzzy time series, Part I. Fuzzy Sets and Systems, 54, 1–10.
  10. Song, Q., & Chisom, B. S. (1994). Forecasting enrollments with fuzzy time series, Part II. Fuzzy Sets and Systems, 62, 1–8.
  11. Chen, S. M. (1996). Forecasting enrollments based on fuzzy time series. Fuzzy Sets and Systems, 81, 311–319.
  12. De Carvalho, F. A. T. (1995). Histograms in Symbolic Data Analysis. Annals of Operations Research, 55, 229–322.
  13. Cazes, P., Chouakria, A., Diday, E., & Schektman, S. (1997). Extension de l’analyse en composantes principales des données de type intervallo. Revue de Statistique Appliquée, 24, 5–24.
  14. Bertrand, P., & Goupil, F. (2000). Descriptive statistics for symbolic data. Springer.
  15. Billard, L., & Diday, E. (2003). From the statistics of data to the statistics of knowledge: Symbolic Data Analysis. Journal of the American Statistical Association, 98(462), 470–487.
  16. Maia, A. L. S., De Carvalho, F. A. T., & Ludermir, T. B. (2008). Forecasting models for interval-valued time series. Neurocomputing, 71(10–12), 3344–3352.
  17. Arroyo, J., & Maté, C. (2006). Introducing interval time series: Accuracy measures. In COMPSTAT 2006, Proceedings in Computational Statistics (pp. 1139–1146).
  18. https://www.academia.edu/download/5886662/pred_simb_mode_accuracy_measures.pdf
  19. Elman, J. (1990). Finding structure in time. Cognitive Science, 15(2), 179–211. https://doi.org/10.1207/s15516709cog1402_1
  20. Chandra, R., & Zhang, M. J. (2012). Cooperative coevolution of Elman recurrent neural networks for chaotic time series prediction. Neurocomputing, 86, 116–123. https://doi.org/10.1016/j.neucom.2012.01.014
  21. Cacciola, M., Megali, G., Pellicano, D., & Morabito, F. C. (2012). Elman neural networks for characterizing voids in welded strips: A study. Neural Computing and Applications, 21, 869–875. https://doi.org/10.1007/s00521-011-0609-3
  22. Wang, J., Zhang, W., Li, Y., Wang, J., & Dang, Z. (2014). Forecasting wind speed using empirical mode decomposition and Elman neural network. Applied Soft Computing, 23, 452–459. https://doi.org/10.1016/j.asoc.2014.06.027
  23. Jang, J. S. R. (1991). Fuzzy modeling using generalized neural networks and Kalman filter algorithm (Oral presentation). In Proceedings of the AAAI’91: Proceedings of the Ninth National Conference on Artificial Intelligence (pp. 914–919). Anaheim, CA, USA.
  24. Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15(1), 116–132. https://doi.org/10.1109/TSMC.1985.6313399
  25. Hwang, J. F., Chen, S.-H., & Lee, C.-H. (1998). Handling forecasting problems using fuzzy time series. Fuzzy Sets and Systems, 100, 217–228. https://doi.org/10.1016/S0165-0114(97)00121-8
  26. Xiong, T., Li, C., & Bao, Y. (2017). Interval-valued time series forecasting using a novel hybrid Holt’ and MSVR model. Economic Modelling, 60, 11–23. https://doi.org/10.1016/j.econmod.2016.08.019
  27. Xiong, T., Bao, Y., & Hu, Z. (2014a). Multiple-output support vector regression with a firefly algorithm for interval-valued stock price index forecasting. Knowledge-Based Systems, 55, 87–100. https://doi.org/10.1016/j.knosys.2013.10.012
  28. Xiong, T., Bao, Y., & Hu, Z. (2014b). Interval forecasting of electricity demand: A novel bivariate EMD-based support vector regression modeling framework. Electrical Power and Energy Systems, 63, 353–362. https://doi.org/10.1016/j.ijepes.2014.06.010
  29. Rodrigues, P. M. M., & Salish, N. (2015). Modeling and forecasting interval time series with threshold models. Advances in Data Analysis and Classification, 9, 41–57. https://doi.org/10.1007/s11634-014-0170-x
  30. Sun, S., Sun, Y., Wang, S., & Wei, Y. (2018). Interval decomposition ensemble approach for crude oil price forecasting. Energy Economics, 76, 274–287. https://doi.org/10.1016/j.eneco.2018.10.015
  31. Xiong, T., Bao, Y., Hu, Z., & Chiong, R. (2015). Forecasting interval time series using a fully complex-valued RBF neural network with DPSO and PSO algorithms. Information Sciences, 305, 77–92. https://doi.org/10.1016/j.ins.2015.01.029
  32. Park, H., & Sakaori, P. (2014). Forecasting symbolic candle chart-valued time series. Communications for Statistical Applications and Methods, 21(6), 471–486. https://doi.org/10.5351/CSAM.2014.21.6.471
  33. Papageorgiou, E. I., & Poczeta, K. (2017). A two-stage model for time series prediction based on fuzzy cognitive maps and neural networks. Neurocomputing, 232, 113–121. https://doi.org/10.1016/j.neucom.2016.10.072
  34. Ichino, M., Yaguchi, H., & Diday, E. (1996). A fuzzy symbolic pattern classifier. In E. Diday et al. (Eds.), Ordinal and symbolic data analysis (pp. 92–102). Springer.
  35. Rasson, J. P., & Lissoir, S. (2000). Symbolic kernel discriminant analysis. In H.-H. Bock & E. Diday (Eds.), Symbolic data analysis (pp. 244–265). Springer. https://doi.org/10.1007/s001800050043
  36. Périnel, E., & Lechevallier, Y. (2000). Symbolic discriminant rules. In H.-H. Bock & E. Diday (Eds.), Analysis of symbolic data (pp. 244–265). Springer.
  37. Bock, H. H. (2001). Clustering algorithms and Kohonen maps for symbolic data. Proceedings of ICNCB, 2001, 203–215.
  38. Chavent, M., & Lechevallier, Y. (2002). Dynamical clustering of interval data: Optimization of an adequacy criterion based on Hausdorff distance. In K. Jajuga, A. Sokołowski, & H. H. Bock (Eds.), Classification, clustering, and data analysis (pp. 55–65). Springer. https://doi.org/10.1007/978-3-642-56181-8_5
  39. Chavent, M., & Sarraco, J. (2008). On central tendency and dispersion measures for intervals and hypercubes. Communications in Statistics-Theory and Methods, 37, 1471–1482. https://doi.org/10.1080/03610920701678984
  40. Irpino, A. (2006). Spaghetti PCA analysis: An extension of principal components analysis to time-dependent interval data. Pattern Recognition Letters, 27, 504–513. https://doi.org/10.1016/j.patrec.2005.09.013
  41. Groenen, P. J. F., Winsberg, S., Rodrigues, O., & Diday, E. (2006). I-SCAL: Multidimensional scaling of interval dissimilarities. Computational Statistics and Data Analysis, 51, 360–378. https://doi.org/10.1016/j.csda.2006.04.003
  42. Gowda, K. C., & Diday, E. (1991). Symbolic clustering using a new dissimilarity measure. Pattern Recognition, 24, 567–578. https://doi.org/10.1016/0031-3203(91)90022-W
  43. Ichino, M., & Yaguchi, H. (1994). Generalized Minkowski metrics for mixed feature type data analysis. IEEE Transactions on Systems, Man, and Cybernetics, 24, 698–708. https://doi.org/10.1109/21.286391
  44. Gowda, K. C., & Ravi, T. R. (1995). Agglomerative clustering of symbolic objects using the concepts of both similarity and dissimilarity. Pattern Recognition Letters, 16, 647–652.https://doi.org/10.1016/0167-8655(95)80010-Q
  45. Gowda, K. C., & Ravi, T. R. (1999). Clustering of symbolic objects using the gravitational approach. IEEE Transactions on Systems, Man, and Cybernetics, 29, 888–894.
  46. Chavent, M. (2000). Criterion-based divisive clustering for symbolic objects. In H.-H. Bock & E. Diday (Eds.), Analysis of symbolic data: Exploratory methods for extracting statistical information from complex data (pp. 299–311). Springer-Verlag.
  47. Guru, D. S., Kiranagi, B. B., & Nagabhushan, P. (2004). Multivalued type proximity measure and concept of mutual similarity value useful for clustering symbolic patterns. Pattern Recognition Letters, 25, 1203–1213. https://doi.org/10.1016/j.patrec.2004.03.016
  48. El-Sonbaty, Y., & Ismail, M. A. (1998). Fuzzy clustering for symbolic data. IEEE Transactions on Fuzzy Systems, 6, 195–204. https://doi.org/10.1109/91.669013
  49. De Carvalho, F. A. T. (2007). Fuzzy c-means clustering methods for interval-valued data. Pattern Recognition Letters, 28, 423–437.
  50. De Carvalho, F. A. T., Csernel, M., & Lechevallier, Y. (2009). Clustering constrained symbolic data. Pattern Recognition Letters, 30, 1037–1045. https://doi.org/10.1016/j.patrec.2009.04.009
  51. De Carvalho, F. A. T., & Lechevallier, Y. (2009a). Partitional clustering algorithms symbolic interval data based on single adaptive distances. Pattern Recognition, 42, 1223–1236. https://doi.org/10.1016/j.patcog.2008.11.016
  52. De Carvalho, F. A. T., & Lechevallier, Y. (2009b). Dynamic clustering of interval-valued data based on adaptive quadratic distances. IEEE Transactions on System, Man, and Cybernetics-Part A: Systems and Humans, 39, 1295–1306. https://doi.org/10.1109/TSMCA.2009.2030167
  53. De Carvalho, F. A. T., De Souza, R. M. C. R., Chavent, M. & Lechevallier, Y. (2006). Adaptive Hausdorff distances and dynamic clustering of symbolic data. Pattern Recognition Letters, vol. 27, pp. 167–179. https://doi.org/10.1016/j.patrec.2005.08.014.
  54. De Souza, R. M. C. R. & De Carvalho, F. A. T. (2004). Clustering of interval data based on city-block distances. Pattern Recognition Letters, vol. 25, pp. 353-365. https://doi.org/10.1016/j.patrec.2003.10.016.
  55. Irpino, A. & Verde, R. (2008). Dynamic clustering of interval data using a Wasserstein-based distance. Pattern Recognition Letters, vol. 29, pp. 1648–1658. https://doi.org/10.1016/j.patrec.2008.04.008.
  56. Lima, Neto E. A. & De Carvalho, F. A. T. (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis, vol.54, pp. 333–347. https://doi.org/10.1016/j.csda.2009.08.010
  57. Arroyo, J. & Mat´e, C. (2009). Forecasting histogram time series with k-nearest neighbors methods. International Journal of Forecasting, vol. 25, pp. 192–207. https://doi.org/10.1016/j.ijforecast.2008.07.003.
  58. Souza, R. M. C. R. & De Carvalho, F. A. T. (2004). Clustering of interval data based on city-block distances. Pattern Recognition Lett., vol. 25, no.3, pp.353-365. https://doi.org/10.1016/j.patrec.2003.10.016.
  59. De Carvalho, F. A. T., Souza, R.M.C.R., Chavent, M. & Lechevallier, Y. (2006). Adaptive Hausdorff distances and dynamic clustering of symbolic data. Pattern Recognition Lett., vol.27, no.3, pp.167-179, 2006. https://doi.org/10.1016/j.patrec.2005.08.014.
  60. Lauro, C. N. & Palumbo, F. (2000). Principal component analysis of interval data: a symbolic data analysis approach. Computational Statistics, vol.15, no.1, pp. 73-87. https://doi.org/10.1007/s001800050038
  61. Billard, L. & Diday, E. (2000). Regression analysis for interval-valued data, Data Analysis, Classification, and Related Methods, in Proceedings of the Seventh Conference of the International Federation of Classification Societies (IFCS’00), pp. 369–374, Springer, Belgium. https://doi.org/10.1007/978-3-642-59789-3_58
  62. Palumbo, F. & Verde, R. (1999). Non-symmetrical factorial discriminant analysis for symbolic objects. Applıed Stochastıc Models ın Busıness and Industry, vol. 15, no. 4, pp. 419-427. https://doi.org/10.1002/(SICI)1526-4025(199910/12)15:4 3.0.CO;2-P.
  63. Lauro, N. C., Verde, R. & Palumbo, F. (2000). Factorial Discriminant Analysis on Symbolic Objects. İn Bock, H.-H., Diday, E. (Eds.), Analysis of Symbolic Data, pp. 212-233, Springer, Heidelberg.
  64. Silva, A., Neto, E. L., & Anjos, U. (2011, August). A regression model to interval-valued variables based on copula approach. In Proceedings of the 58th world statistics congress of the international statistical institute (pp. 6481-6486). Ireland, pp. 6481–6486: Dublin.
  65. Clerc, M. (2005). Particle Swarm Optimization, ISTE, U.S.A.
  66. Kröse, B. & van der Smagt, P. (1996). Introduction to Neural Network, The University of Amsterdam.
  67. Siddique, N. & Adeli, H. (2013). Computational Intelligence, Wiley.
  68. Shi, Y. & Eberhart, R. C. (1999). The empirical study of particle swarm optimization. In IEEE Proceedings of the 1999 congress on evolutionary computation-CEC99 (Cat. No. 99TH8406), Vol. 3, pp. 1945-1950. DOI: 10.1109/CEC.1999.785511.
  69. Chang, S. C., Chuang, W. C., & Jeng, J. T. (2023). New Interval Improved Fuzzy Partitions Fuzzy C-Means Clustering Algorithms under Different Distance Measures for Symbolic Interval Data Analysis. Applied Sciences, 13(22), 12531. https://doi.org/10.3390/app132212531.
  70. Jiang, P., Liu, Z., Niu, X., & Zhang, L. (2021). A combined forecasting system based on statistical methods, artificial neural networks, and deep learning methods for short-term wind speed forecasting. Energy, 217, 119361. https://doi.org/10.1016/j.energy.2020.119361.
  71. Chinnadurrai, C. L., Udaiyakumar, S., & Ravindran, S. (2024). Ensemble Deep Learnıng Approach Based On Wavelet Transform And Recurrent Neural Networks For Wınd Speed Forecastıng. Ijest, 18(1), 26.
  72. Wu, C., Li, J., Liu, W., He, Y., & Nourmohammadi, S. (2023). Short-term electricity demand forecasting using a hybrid ANFIS–ELM network optimized by an improved parasitism–predation algorithm. Applied Energy, 345, 121316. https://doi.org/10.1016/j.apenergy.2023.121316.
  73. Wan, S., & Dong, J. (2020). A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making. Decision-Making Theories and Methods Based on Interval-Valued Intuitionistic Fuzzy Sets, 1-35. https://doi.org/10.1007/978-981-15-1521-7_1.
  74. Haiyun, C., Zhixiong, H., Yüksel, S., & Dinçer, H. (2021). Analysis of the innovation strategies for green supply chain management in the energy industry using the QFD-based hybrid interval-valued intuitionistic fuzzy decision approach. Renewable and Sustainable Energy Reviews, 143, 110844. https://doi.org/10.1016/j.rser.2021.110844.
  75. Ali, Z., Mahmood, T., Ullah, K., & Khan, Q. (2021). Einstein geometric aggregation operators using a novel complex interval-valued Pythagorean fuzzy setting with application in green supplier chain management. Reports in Mechanical Engineering, 2(1), 105-134. DOI: https://doi.org/10.31181/rme2001020105t.
  76. Garg, H., & Kumar, K. (2020). A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory. Artificial Intelligence Review, 53, 595-624. https://doi.org/10.1007/s10462-018-9668-5.
  77. Sen Z., (2004). Yapay sinir ağları ilkeleri, Turkish Water Foundation Publications, İstanbul.
  78. Sen Z., (2009). Bulanık mantık ilkeleri ve modelleme. Turkish Water Foundation Publications, İstanbul.