Abstract
In this study, a fuzzy arithmetics-based fuzzy time series modeling method is introduced. After input data normalization, the fuzzy c-means clustering algorithm is used for fuzzification and establishment of antecedents of the fuzzy rules. Here, each rule consequent is treated as a fuzzy number composed of a left and a right hand side fuzzy set, each of which is given by a sigmoid membership function. The novelty of the proposed method lies in the application of pliant arithmetics to aggregate separately the left and the right hand sides of the individual fuzzy consequents, taking the activation levels of the corresponding antecedents into account. Here, Dombi’s conjunction operator is applied to form the fuzzy output from the aggregates of the left and right hand side sigmoid functions. The introduced defuzzification method does not require any numerical integration and runs in constant time. The output of the pliant arithmetic based fuzzy time series model is obtained by denormalizing the crisp output produced by the fuzzy inference. Lastly, the modeling capability of the introduced methodology was tested on empirical data. Based on these results, our method may be viewed as a viable alternative prediction technique.
Dedicated to the memory of Csanád Imreh
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References
Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming: Theory and Algorithms, 3rd edn. Wiley, New Jersey (2006)
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Caliński, T., Harabasz, J.: A dendrite method for cluster analysis. Commun. Stat. Simul. Comput. 3(1), 1–27 (1974)
Dombi, J.: Towards a general class of operators for fuzzy systems. IEEE Trans. Fuzzy Syst. 16(2), 477–484 (2008)
Dombi, J.: Pliant arithmetics and pliant arithmetic operations. Acta Polytech. Hung. 6(5), 19–49 (2009)
Dombi, J., Szépe, T.: Pliant control system: implementation. In: IEEE 8th International Symposium on Intelligent Systems and Informatics, pp. 225–230 (2010)
Hyndman, R.J., Khandakar, Y.: Automatic time series forecasting: the forecast package for R. J. Stat. Softw. 27(3), 1–22 (2008)
Li, S.T., Cheng, Y.C., Lin, S.Y.: A FCM-based deterministic forecasting model for fuzzy time series. Comput. Math. Appl. 54(12), 3052–3063 (2008)
Song, Q., Chissom, B.: Fuzzy time series and its models. Fuzzy Sets Syst. 54, 269–277 (1993)
Tanii, H., Nakajima, H., Tsuchiya, N., Kuramoto, K., Kobashi, S., Hata, Y.: A fuzzy-AR model to predict human body weights. In: 2012 IEEE International Conference on Fuzzy Systems, pp. 1–6 (2012)
Valenzuela, O., Rojas, I., Rojas, F., Pomares, H., Herrera, L., Guillen, A., Marquez, L., Pasadas, M.: Hybridization of intelligent techniques and ARIMA models for time series prediction. Fuzzy Sets Syst. 159, 821–845 (2008)
Štĕpnička, M., Dvořák, A., Pavliska, V., Vavříčková, L.: A linguistic approach to time series modeling with the help of F-transform. Fuzzy Sets Syst. 180(1), 164–184 (2011)
Yu, H.K.: Weighted fuzzy time series models for TAIEX forecasting. Phys. A: Stat. Mech. Appl. 349(3–4), 609–624 (2005)
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Dombi, J., Jónás, T., Tóth, Z.E. (2017). A Pliant Arithmetic-Based Fuzzy Time Series Model. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2017. Lecture Notes in Computer Science(), vol 10306. Springer, Cham. https://doi.org/10.1007/978-3-319-59147-6_12
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DOI: https://doi.org/10.1007/978-3-319-59147-6_12
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