Abstract
In fuzzy time series (FTS) based forecasting models, FTS is utilized to depict the characteristic of time series. In the constructed FTS of the existing models, each moment consists of a fuzzy set to reflect the size range of data and aligns with people’s semantic description. However, this FTS ignores some essential fuzzy information, for example the membership degree of data to fuzzy set, and then it fails to describe the feature of time series accurately and limits forecasting performance. To address these issues, ordered pair FTS is proposed in this study. This FTS is consisted of ordered pairs, including two aspects: the fuzzified fuzzy set of data and corresponding membership degree. Worth noting that the ordered pair FTS not only captures the characteristic of data accurately by making use of the information of fuzzy set, but also maintains its interpretability. Following this, ordered pair fuzzy logical relationship (FLR) is derived from antecedent ordered pair(s) to a consequent ordered pair, it describes the association of time series effectively through capturing data information exactly. Based on the ordered pair FLR, a forecasting model is designed. This model applies fuzzy implication to measure the truth degree of FLR and indicate the importance of each fuzzy rule in prediction, ultimately produces reasonable prediction result. The superiorities of the proposed ordered pair FTS and forecasting model are demonstrated in experimental studies, where they are compared with other existing forecasting models.
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References
Fu A, Liu J, Zhang TL (2022) Self-stacking random weight neural network with multi-layer features fusion. Int J Mach Learn Cybern 13:1945–1957
Brenjkar E, Delijani EB, Karroubi K (2021) Prediction of penetration rate in drilling operations: a comparative study of three neural network forecast methods. J Pet Explor Prod 11(2):805–818
Xie Z, Li Y (2019) Large-scale support vector regression with budgeted stochastic gradient descent. Int J Mach Learn Cybern 10:1529–1541
Das SP et al (2018) A novel hybrid model using teaching-learning-based optimization and a support vector machine for commodity futures index forecasting. Int J Mach Learn Cybern 9:97–111
Lu W, Yang JH, Liu XD, Pedrycz W (2014) The modeling and prediction of time series based on synergy of high-order fuzzy cognitive map and fuzzy c-means clustering. Knowl-Based Syst 70:242–255
Mansouri T, Zareravasan A, Ashrafi A (2021) A learning fuzzy cognitive map (LFCM) approach to predict student performance. J Inf Technol Educ Res 20:221–243
Xian SD, Li TJ, Cheng Y (2020) A novel fuzzy time series forecasting model based on the hybrid wolf pack algorithm and ordered weighted averaging aggregation operator. Int J Fuzzy Syst 22(6):1832–1850
Bose M, Mali K (2018) A novel data partitioning and rule selection technique for modeling high-order fuzzy time series. Apply Soft Comput 63:87–96
Tahseen AJ, Syed MAB (2008) A refined fuzzy time series model for stock market forecasting. Physica A 387(12):2857–2862
Wang JZ, Li HM, Lu HY (2018) Application of a novel early warning system based on fuzzy time series in urban air quality forecasting in China. Apply Soft Comput 71:783–799
Abhishekh, Gautam SS, Singh SR (2018) A refined method of forecasting based on high-order intuitionistic fuzzy time series data. Prog Artif Intell 7(4):339–350
Ha CN, Tai VV, Thao NT (2018) An improved fuzzy time series forecasting model. In: International econometric conference of Vietnam, pp 474–490
Wu H, Long H, Jiang J (2019) Handling forecasting problems based on fuzzy time series model and model error learning. Apply Soft Comput 78:109–118
Severiano CA, Silva P, Cohen M, Guimarães F (2021) Evolving fuzzy time series for spatio-temporal forecasting in renewable energy systems. Renew Energy 171:764–793
Yu THK, Huarng KH (2008) A bivariate fuzzy time series model to forecast the TAIEX. Expert Syst Appl 34(4):2945–2952
Song Q, Chissom BS (1991) Forecasting enrollments with fuzzy time series: part I. In: The annual meeting of the mid-south educational research association, Lexington, KY
Song Q, Chissom BS (1993) Forecasting enrollments with fuzzy time series—part I. Fuzzy Sets Syst 54(1):1–9
Azahari SNF, Saian R, Othman M (2017) Forecasting rainfall based on fuzzy time series sliding window model, vol 2. Springer, Singapore, pp 143–153
Xian SD, Zhang JF, Xiao Y, Pang J (2018) A novel fuzzy time series forecasting method based on the improved artificial fish swarm optimization algorithm. Soft Comput 22:3907–3917
Wang LZ, Liu XD, Pedrycz W (2013) Effective intervals determined by information granules to improve forecasting in fuzzy time series. Expert Syst Appl 40(14):5673–5679
Sanjay K, Sukhdev SG (2016) Intuitionistic fuzzy time series: an approach for handling nondeterminism in time series forecasting. IEEE Trans Fuzzy Syst 24(6):1270–1281
Zhang WY, Zhang SX, Zhang S, Yu DJ, Huang NN (2018) A novel method based on FTS with both GA-FCM and multifactor BPNN for stock forecasting. Soft Comput 23:6979–6994
Li F, Yu FS (2018) A long-association relationship based forecasting method for time series. In: 14th international conference on natural computation, fuzzy systems and knowledge discovery, pp 548–554
Yang XY, Yu FS, Pedrycz W (2017) Long-term forecasting of time series based on linear fuzzy information granules and fuzzy inference system. Int J Approx Reason 81:1–27
Tai V, Nghiep L (2019) A new fuzzy time series model based on cluster analysis problem. Int J Fuzzy Syst 21(3):852–864
Bisht KL, Kumar SJ (2016) Fuzzy time series forecasting method based on hesitant fuzzy sets. Expert Syst Appl 64:557–568
Dincer NG (2018) A new fuzzy time series model based on fuzzy c-regression model. Int J Fuzzy Syst 20(6):1872–1887
Saxena P, Sharma K, Easo S (2012) Forecasting enrollments based on fuzzy time series with higher forecast accuracy rate. Int J Comput Technol Appl 3(3):957–961
Guo HY, Pedrycz W, Liu XD (2019) Fuzzy time series forecasting based on axiomatic fuzzy set theory. Neural Comput Appl 31:3921–3932
Bas E, Grosan C, Egrioglu E, Yolcu U (2018) High order fuzzy time series method based on pi-sigma neural network. Eng Appl Artif Intell 72:350–356
Guo HJ, Dai ZL, Guan S, Zhao AW (2018) Forecasting model based on heuristic learning of high-order fuzzy-trend and jump rules. J Intell Fuzzy Syst 35:257–267
Yu HK (2005) Weighted fuzzy time series models for TAIEX forecasting. Physica A 349(3–4):609–624
Teoh HJ, Chen TL, Cheng CH (2007) Frequency-weighted fuzzy time series based on Fibonacci sequence for TAIEX forecasting. In: Emerging technologies in knowledge discovery and data mining, pp 27–34
Qiu WR, Liu XD, Li HL (2011) A generalized method for forecasting based on fuzzy time series. Expert Syst Appl 38(8):10446–10453
Cheng CH, Chen CH (2018) Fuzzy time series model based on weighted association rule for financial market forecasting. Expert Syst Int J Knowl Eng 35(4):e12271
Singh P (2018) Rainfall and financial forecasting using fuzzy time series and neural networks based model. Int J Mach Learn Cybern 9:491–506
Singh P (2017) A brief review of modeling approaches based on fuzzy time series. Int J Mach Learn Cybern 8:397–420
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Zeng XY, Shu L, Huang GM, Jiang J (2016) Triangular fuzzy series forecasting based on grey model and neural network. Appl Math Model 40:1717–1727
Zhou HJ (2021) Two general construction ways toward unified framework of ordinal sums of fuzzy implications. IEEE Trans Fuzzy Syst 29(4):846–860
Shi Y (2021) Interval Information content of fuzzy relation and the application in the fuzzy implication operators. J Math 2021:1–11
Li F, Pei DW (2017) Multiple fuzzy implications and their generating methods. Springer, London
Jiang P, Dong QL, Li PZ, Lian LL (2017) A novel high-order weighted fuzzy time series model and its application in nonlinear time series prediction. Apply Soft Comput 55:44–62
Yang R, He J, Xu M et al (2018) An intelligent and hybrid weighted fuzzy time series model based on empirical mode decomposition for financial markets forecasting. In: Industrial conference on data mining. Springer, Cham, pp 105–118
Aladag CH, Egrioglu E (2014) A high order seasonal fuzzy time series model and application to international tourism demand of turkey. J Intell Fuzzy Syst 26:295–302
Babu CN, Reddy BE (2014) A moving-average filter based hybrid ARIMA-ANN model for forecasting time series data. Appl Soft Comput 23:27–38
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 12201396) and the Science and Technology Commission of Shanghai Municipality-Shanghai Local University Capacity Building Project (No. 23010502100).
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Li, F., Yang, X. A novel forecasting model based on the raised ordered pair fuzzy time series and fuzzy implication. Int. J. Mach. Learn. & Cyber. 15, 1873–1890 (2024). https://doi.org/10.1007/s13042-023-02003-4
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DOI: https://doi.org/10.1007/s13042-023-02003-4