Research Article
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Deep Fuzzy Functions Approach for Time Series Forecasting

Year 2025, Volume: 26 Issue: 4, 680 - 698

Ali Zafer Dalar

https://doi.org/10.37880/cumuiibf.1749594

Abstract

In this study, a novel forecasting method is proposed by integrating classical type-1 fuzzy functions with deep learning models based on Long Short-Term Memory (LSTM) networks, aiming to enhance forecast accuracy and systematically address uncertainty in time series data. In the developed approach, an independent LSTM model is constructed for each fuzzy cluster, and these models are trained using lagged variables derived from the time series. During the forecasting phase, the output of each model is weighted according to the degree of membership of the corresponding observation to its respective cluster, and the final prediction is computed accordingly. In this way, the proposed Deep Fuzzy Forecasting Functions (DBF) approach simultaneously captures both the dynamic temporal patterns of the series and the structural uncertainty among observations. The training process employs the Adam optimization algorithm, and various combinations of hyperparameters—including the number of epochs, the number of hidden units, the number of clusters, and the α-cut threshold—were experimentally tested. The optimal configuration was determined based on empirical performance. The proposed DBF approach was evaluated on time series datasets with distinct characteristics, including financial and meteorological data, and benchmarked against widely used forecasting methods. Experimental results demonstrated that the proposed DBF model achieved the lowest prediction errors in many scenarios and delivered high accuracy, particularly for short- and medium-term forecasts. These findings indicate that the developed approach is flexible, generalizable, and effective as a forecasting tool across various domains.

Keywords

Time series forecasting Fuzzy inference systems Long short-term memory Artificial neural networks

Project Number

FEN-BAP-A-250221-36

References

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  • Aladag, C. H. (2013). Using multiplicative neuron model to establish fuzzy logic relationships. Expert Systems with Applications, 40(3). https://doi.org/10.1016/j.eswa.2012.05.039
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  • Bas, E., & Egrioglu, E. (2022). A fuzzy regression functions approach based on Gustafson-Kessel clustering algorithm. Information Sciences, 592, 206-214.
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Zaman Serisi Öngörüsü için Derin Bulanık Fonksiyonlar Yaklaşımı

Year 2025, Volume: 26 Issue: 4, 680 - 698

Ali Zafer Dalar

https://doi.org/10.37880/cumuiibf.1749594

Abstract

Bu çalışmada, zaman serisi öngörülerinde doğruluk düzeyini artırmak ve verideki belirsizlikleri yapılandırılmış biçimde dikkate almak amacıyla, klasik tip-1 bulanık fonksiyonlar yaklaşımı ile uzun kısa süreli bellek (LSTM) temelli derin öğrenme modellerinin bir araya getirildiği yeni bir öngörü yöntemi geliştirilmiştir. Geliştirilen yöntemde, her bir bulanık kümeye karşılık gelen bağımsız LSTM modelleri yapılandırılmış ve bu modeller, belirli gecikmeli değişkenlere dayalı olarak eğitilmiştir. Öngörü sürecinde, her bir modelin çıktısı, ilgili gözlemin kümelere aitlik dereceleri ile ağırlıklandırılarak nihai tahmin değeri (öngörü) elde edilmiştir. Bu sayede, önerilen derin bulanık öngörü fonksiyonları (DBF) yaklaşımı ile hem zaman serisinin dinamik örüntülerini hem de gözlemler arasındaki belirsizlikleri aynı anda dikkate alınabilmiştir. Modelin eğitimi sürecinde Adam optimizasyon algoritması kullanılmış ve epoch sayısı, gizli birim sayısı, küme sayısı ile α-kesim katsayısı gibi hiperparametreler çeşitli kombinasyonlar halinde test edilmiştir. En uygun parametre ayarları deneysel olarak belirlenmiştir. Önerilen DBF yaklaşımı, farklı özelliklere sahip finansal ve meteorolojik zaman serisi veri kümeleri üzerinde değerlendirilmiş ve mevcut öngörü yöntemleri ile karşılaştırılmıştır. Uygulama sonuçlarında, önerilen DBF yönteminin pek çok senaryoda en düşük öngörü hatasını verdiği ve özellikle kısa ve orta vadeli öngörülerde yüksek başarı sağladığı görülmüştür. Bu bulgular, geliştirilen yaklaşımın genellenebilirliğe sahip, esnek ve kararlı bir öngörü çerçevesi sunduğunu ve çeşitli alanlarda kullanılabilecek nitelikte olduğunu göstermektedir.

Keywords

Zaman serisi öngörüsü Bulanık çıkarım sistemleri Uzun kısa süreli bellek Yapay sinir ağları

Ethical Statement

Bu çalışmanın hazırlanma sürecinde bilimsel ve etik ilkelere uyulduğu ve yararlanılan tüm çalışmaların kaynakçada belirtildiği beyan olunur.

Supporting Institution

Giresun Üniversitesi

Project Number

FEN-BAP-A-250221-36

References

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  • Aladag, C. H. (2013). Using multiplicative neuron model to establish fuzzy logic relationships. Expert Systems with Applications, 40(3). https://doi.org/10.1016/j.eswa.2012.05.039
  • Aladag, C. H., Turksen, I. B., Dalar, A. Z., Egrioglu, E., & Yolcu, U. (2014). Application of Type-1 Fuzzy Functions Approach for Time Series Forecasting. TJFS: Turkish Journal of Fuzzy Systems An Official Journal of Turkish Fuzzy Systems Association, 5(1), 1309-1190.
  • Alateeq, M., & Pedrycz, W. (2024). Logic-oriented fuzzy neural networks: A survey. Expert Systems with Applications, 257, 125120. https://doi.org/10.1016/j.eswa.2024.125120
  • AL-Sukeinee, R. J., & Khudeyer, R. S. (2024). Review: Deep Learning and Fuzzy Logic Applications. Engineering and Technology Journal, 09(06). https://doi.org/10.47191/etj/v9i06.09
  • Bas, E., & Egrioglu, E. (2022). A fuzzy regression functions approach based on Gustafson-Kessel clustering algorithm. Information Sciences, 592, 206-214.
  • Bas, E., Egrioglu, E., Aladag, C. H., & Yolcu, U. (2015). Fuzzy-time-series network used to forecast linear and nonlinear time series. Applied Intelligence, 43, 343-355. https://doi.org/10.1007/s10489-015-0647-0
  • Bas, E., Grosan, C., Egrioglu, E., & Yolcu, U. (2018). High order fuzzy time series method based on pi-sigma neural network. Engineering Applications of Artificial Intelligence, 72, 350-356. https://doi.org/10.1016/j.engappai.2018.04.017
  • Baser, F., & Demirhan, H. (2017). A fuzzy regression with support vector machine approach to the estimation of horizontal global solar radiation. Energy, 123, 229-240. https://doi.org/10.1016/j.energy.2017.02.008
  • Beyhan, S., & Alci, M. (2010). Stable modeling based control methods using a new RBF network. ISA Transactions, 49(4), 510-518. https://doi.org/10.1016/j.isatra.2010.04.005
  • Beyhan, S., & Alci, M. (2011). Extended fuzzy function model with stable learning methods for online system identification. International Journal of Adaptive Control and Signal Processing, 25(2). https://doi.org/10.1002/acs.1214
  • Bezdek, J. C., Ehrlich, R., & Full, W. (1984). FCM: The fuzzy c-means clustering algorithm. Computers & geosciences, 10(2-3), 191-203.
  • Box, G. E. P., & Jenkins, G. M. (1976). Time Series Analysis: Forecasting and Control. Içinde Holden-Day series in time series analysis and digital processing (Rev. ed.). Holden-Day. https://books.google.com.tr/books?id=1WVHAAAAMAAJ
  • Cagcag Yolcu, O., & Yolcu, U. (2024). A new ensemble intuitionistic fuzzy-deep forecasting model: Consolidation of the IFRFs-bENR with LSTM. Information Sciences, 679. https://doi.org/10.1016/j.ins.2024.121007
  • Celikyilmaz, A., & Turksen, I. B. (2007). Fuzzy functions with support vector machines. Information Sciences, 177(23), 5163-5177. https://doi.org/10.1016/j.ins.2007.06.022
  • Celikyilmaz, A., & Turksen, I. B. (2008). Enhanced fuzzy system models with improved fuzzy clustering algorithm. IEEE Transactions on Fuzzy Systems, 16(3), 779-794.
  • Celikyilmaz, A., Turksen, I. B., & Kacprzyk, J. (2009). Modeling Uncertainty with Fuzzy Logic: With Recent Theory and Applications. Içinde Studies in Fuzziness and Soft Computing (C. 240). Springer-Verlag Berlin Heidelberg. https://books.google.com.tr/books?id=Xj1vCQAAQBAJ
  • Chakravarty, S., Demirhan, H., & Baser, F. (2020). Fuzzy regression functions with a noise cluster and the impact of outliers on mainstream machine learning methods in the regression setting. Applied Soft Computing, 96, 106535. https://doi.org/https://doi.org/10.1016/j.asoc.2020.106535
  • Chakravarty, S., Demirhan, H., & Baser, F. (2022a). Modified fuzzy regression functions with a noise cluster against outlier contamination. Expert Systems with Applications, 205. https://doi.org/10.1016/j.eswa.2022.117717
  • Chakravarty, S., Demirhan, H., & Baser, F. (2022b). Robust wind speed estimation with modified fuzzy regression functions with a noise cluster. Energy Conversion and Management, 266. https://doi.org/10.1016/j.enconman.2022.115815
  • Chen, S. (1996). Forecasting enrollments based on fuzzy time series. Fuzzy Sets and Systems, 81(3), 311-319. https://doi.org/10.1016/0165-0114(95)00220-0
  • Dalar, A. Z. (2023). Ensemble Based Type-1 Fuzzy Functions Approach for Time Series Forecasting. Içinde S. Küçükkolbaşı (Ed.), 2023 Proceedings of International E-Conference on Mathematical and Statistical Sciences: A Selcuk Meeting (ss. 78-78). Selçuk University.
  • Dalar, A. Z., & Egrioglu, E. (2018). Bootstrap Type-1 Fuzzy Functions Approach for Time Series Forecasting. Içinde M. Tez & D. von Rosen (Ed.), Trends and Perspectives in Linear Statistical Inference (ss. 69-87). Springer, Cham. https://doi.org/10.1007/978-3-319-73241-1_5
  • Dalar, A. Z., & Egrioglu, E. (2025). Blending traditional and novel techniques: Hybrid type-1 fuzzy functions for forecasting. Engineering Applications of Artificial Intelligence, 148, 110445. https://doi.org/10.1016/J.ENGAPPAI.2025.110445
  • Demirhan, H., & Baser, F. (2024). Hierarchical fuzzy regression functions for mixed predictors and an application to real estate price prediction. Neural computing & applications (Print), 36, 11545-11561. https://doi.org/10.1007/s00521-024-09673-3
  • Demirkan Piskin, M., & Bas, E. (2022). Forecasting Monthly Housing Sales to Foreigners with Type 1 Fuzzy Regression Functions Approach Based on Ridge Regression. Karadeniz Fen Bilimleri Dergisi, 12(2). https://doi.org/10.31466/kfbd.1074832
  • Ducange, P., Fazzolari, M., & Marcelloni, F. (2020). An overview of recent distributed algorithms for learning fuzzy models in Big Data classification. Journal of Big Data, 7(1). https://doi.org/10.1186/s40537-020-00298-6
  • Egrioglu, E., Aladag, C. H., Yolcu, U., & Bas, E. (2014). A new adaptive network based fuzzy inference system for time series forecasting. Aloy Journal of Soft Computing and Applications, 2(1), 25-32.
  • Egrioglu, E., & Bas, E. (2023). Robust intuitionistic fuzzy regression functions approaches. Information Sciences, 638. https://doi.org/10.1016/j.ins.2023.118992
  • Egrioglu, E., Fildes, R., & Bas, E. (2022). Recurrent fuzzy time series functions approaches for forecasting. Granular Computing, 7(1). https://doi.org/10.1007/s41066-021-00257-3
  • Egrioglu, E., Yolcu, U., & Bas, E. (2019). Intuitionistic high-order fuzzy time series forecasting method based on pi-sigma artificial neural networks trained by artificial bee colony. Granular Computing, 4(4). https://doi.org/10.1007/s41066-018-00143-5
  • Fernández, A., Carmona, C. J., del Jesus, M. J., & Herrera, F. (2016). A View on Fuzzy Systems for Big Data: Progress and Opportunities. International Journal of Computational Intelligence Systems, 9. https://doi.org/10.1080/18756891.2016.1180820
  • Gawlikowski, J., Tassi, C. R. N., Ali, M., Lee, J., Humt, M., Feng, J., Kruspe, A., Triebel, R., Jung, P., Roscher, R., Shahzad, M., Yang, W., Bamler, R., & Zhu, X. X. (2023). A survey of uncertainty in deep neural networks. Artificial Intelligence Review, 56(S1), 1513-1589. https://doi.org/10.1007/s10462-023-10562-9
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  • Hamilton, J. D. (1994). Time Series Analysis Princeton University Press. Içinde Princeton, NJ.
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Details

Primary Language Turkish
Subjects Econometric and Statistical Methods, Time-Series Analysis, Statistics (Other)
Journal Section Makaleler
Authors

Ali Zafer Dalar 0000-0002-8574-461X

Project Number FEN-BAP-A-250221-36
Early Pub Date October 22, 2025
Publication Date October 27, 2025
Submission Date July 23, 2025
Acceptance Date October 8, 2025
Published in Issue Year 2025 Volume: 26 Issue: 4

Cite

APA Dalar, A. Z. (2025). Zaman Serisi Öngörüsü için Derin Bulanık Fonksiyonlar Yaklaşımı. Cumhuriyet Üniversitesi İktisadi Ve İdari Bilimler Dergisi, 26(4), 680-698. https://doi.org/10.37880/cumuiibf.1749594
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