Keywords:-

Keywords: Fuzzy Time Series, Multilayer Perceptron, Hesitant Fuzzy Set, High-Order Hesitant Fuzzy Time Series, Air Pollution Forecasting, Accuracy Metric

Article Content:-

Abstract

This study introduces an advanced hybrid model integrating High-Order Hesitant Fuzzy Time Series (HOHFTS) with a Multilayer Perceptron (MLP) to improve the accuracy of air pollutant concentration forecasting. The model utilizes Hesitant Fuzzy Sets to define fuzzy sets, mean aggregated membership values to handle hesitant fuzzy elements, and MLP neural networks to capture complex relationships. A distinguishing feature is the determination of the optimal fuzzy time series (FTS) order, set to 24 in this study, to effectively capture daily temporal dependencies in the hourly air pollutant data. A case study using Semarang City’s air pollution dataset demonstrates the model's effectiveness, with preprocessing addressing missing values and interval-based discretization. Performance evaluation with Mean Absolute Error (MAE) and Symmetric Mean Absolute Percentage Error (SMAPE) indicates outstanding accuracy, with SMAPE values below 10% for most pollutants. Further exploration of hyperparameter optimization and order determination is recommended to enhance generalization and computational efficiency.

References:-

References

Q. Song and B. S. Chissom, “Forecasting enrollments with fuzzy time series — Part I,” Fuzzy Sets Syst, vol. 54, no. 1, pp. 1–9, 1993, doi: 10.1016/0165-0114(93)90355-L.

Q. Song and B. S. Chissom, “Forecasting enrollments with fuzzy time series — part II,” Fuzzy Sets Syst, vol. 62, no. 1, pp. 1–8, 1994, doi: 10.1016/0165-0114(94)90067-1.

S.-M. Chen, “Forecasting enrollments based on high-order fuzzy time series,” Cybern Syst, vol. 33, no. 1, pp. 1–16, Jan. 2002, doi: 10.1080/019697202753306479.

V. Torra, “Hesitant fuzzy sets,” International Journal of Intelligent Systems, vol. 25, no. 6, pp. 529–539, Jun. 2010, doi: 10.1002/int.20418.

R. M. Pattanayak, S. Panigrahi, and H. S. Behera, “High-Order Fuzzy Time Series Forecasting by Using Membership Values Along with Data and Support Vector Machine,” Arab J Sci Eng, vol. 45, no. 12, pp. 10311–10325, Dec. 2020, doi: 10.1007/s13369-020-04721-1.

R. M. Pattanayak, H. S. Behera, and S. Panigrahi, “A novel high order hesitant fuzzy time series forecasting by using mean aggregated membership value with support vector machine,” Inf Sci (N Y), vol. 626, pp. 494–523, May 2023, doi: 10.1016/j.ins.2023.01.075.

S. Abirami and P. Chitra, “Chapter Fourteen - Energy-efficient edge based real-time healthcare support system,” Advances in Computers, vol. 117, no. 1, pp. 339–368, 2020, doi: 10.1016/bs.adcom.2019.09.007.

X. Feng, G. Ma, S.-F. Su, C. Huang, M. K. Boswell, and P. Xue, “A multi-layer perceptron approach for accelerated wave forecasting in Lake Michigan,” Ocean Engineering, vol. 211(107526), pp. 1–11, Sep. 2020, doi: 10.1016/j.oceaneng.2020.107526.

L. Persson et al., “Outside the Safe Operating Space of the Planetary Boundary for Novel Entities,” Environ Sci Technol, vol. 56, no. 3, pp. 1510–1521, Feb. 2022, doi: 10.1021/acs.est.1c04158.

J. Schmale, D. Shindell, E. von Schneidemesser, I. Chabay, and M. Lawrence, “Air pollution: Clean up our skies,” Nature, vol. 515, no. 7527, pp. 335–337, 2014, doi: 10.1038/515335a.

World Health Organization, “WHO Global Air Quality Guidelines,” Geneva, 2021.

A. T. Chan, “Indoor-outdoor relationships of particulate matter and nitrogen oxides under different outdoor meteorological conditions,” Atmos Environ, vol. 36, no. 9, pp. 1543–1551, 2002, doi: 10.1016/S1352-2310(01)00471-X.

World Health Organization, “Ambient (outdoor) air pollution.”

United Nation Environment Program, “Pollution Action Note – Data you need to know.”

D. Saini, P. Dixit, D. H. Lataye, R. K. Rai, and V. M. Motghare, “Assessment of ambient air quality status of Amravati city using time series forecasting network in deep learning MATLAB,” Sādhanā, vol. 49, no. 150, pp. 1–14, Feb. 2024, doi: 10.1007/s12046-024-02500-4.

E. Marinov, D. Petrova-Antonova, and S. Malinov, “Time Series Forecasting of Air Quality: A Case Study of Sofia City,” Atmosphere (Basel), vol. 13, no. 5, pp. 1–19, May 2022, doi: 10.3390/atmos13050788.

A. Hasnain et al., “Time Series Analysis and Forecasting of Air Pollutants Based on Prophet Forecasting Model in Jiangsu Province, China,” Front Environ Sci, vol. 10, pp. 1–12, Jul. 2022, doi: 10.3389/fenvs.2022.945628.

G. Reikard, “Volcanic emissions and air pollution: Forecasts from time series models,” Atmos Environ X, vol. 1(100001), pp. 1–7, Jan. 2019, doi: 10.1016/j.aeaoa.2018.100001.

E. Bas, C. Grosan, E. Egrioglu, and U. Yolcu, “High order fuzzy time series method based on pi-sigma neural network,” Eng Appl Artif Intell, vol. 72, pp. 350–356, 2018, doi: https://doi.org/10.1016/j.engappai.2018.04.017.

M. Xia and Z. Xu, “Hesitant fuzzy information aggregation in decision making,” International Journal of Approximate Reasoning, vol. 52, no. 3, pp. 395–407, Mar. 2011, doi: 10.1016/j.ijar.2010.09.002.

K. Bisht and S. Kumar, “Fuzzy time series forecasting method based on hesitant fuzzy sets,” Expert Syst Appl, vol. 64, pp. 557–568, Dec. 2016, doi: 10.1016/j.eswa.2016.07.044.

A. Chatterjee, J. Saha, and J. Mukherjee, “Clustering with multi-layered perceptron,” Pattern Recognit Lett, vol. 155, pp. 92–99, Mar. 2022, doi: 10.1016/j.patrec.2022.02.009.

Y. Bengio, Y. Lecun, and G. Hinton, “Deep learning for AI,” Commun ACM, vol. 64, no. 7, pp. 58–65, Jun. 2021, doi: 10.1145/3448250.

Y. Lecun, Y. Bengio, and G. Hinton, “Deep learning,” Nature, vol. 521, no. 7553, pp. 436–444, May 2015, doi: 10.1038/nature14539.

I. Saputra and D. A. Kristiyanti, Machine Learning untuk Pemula, 1st ed. Bandung: Informatika, 2022.

I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning. Cambridge, Massachusetts: MIT Press, 2016.

R. Sarno, S. I. Sabilla, Malikhah, D. P. Purbawa, and M. S. H. Ardani, Machine Learning dan Deep Learning-Konsep dan Pemrograman Python, 1st ed., vol. 1. Yogyakarta: Penerbit ANDI, 2023. [Online]. Available:

https://books.google.co.id/books?id=byWFEAAAQBAJ

G. Ciulla and A. D’Amico, “Building energy performance forecasting: A multiple linear regression approach,” Appl Energy, vol. 253(113500), pp. 1–16, Nov. 2019, doi: 10.1016/j.apenergy.2019.113500.

S. Makridakis and M. Hibon, “The M3-Competition: results, conclusions and implications,” 2000. [Online]. Available: www.elsevier.com/locate/ijforecast

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Prasetyo, K., Warsito, B., & Surarso, B. (2025). A Hybrid Model High-Order Hesitant Fuzzy Time Series and Multilayer Perceptron with Mean Aggregated Membership Value for Enhanced Air Pollutant Concentration Forecasting. International Journal Of Mathematics And Computer Research, 13(1), 4795-4801. https://doi.org/10.47191/ijmcr/v13i1.11