A new deep intuitionistic fuzzy time series forecasting method based on long short-term memory
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A new deep intuitionistic fuzzy time series forecasting method based on long short‑term memory Cem Kocak1 · Erol Egrioglu2 · Eren Bas2 Accepted: 29 October 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In recent years, deep artificial neural networks can have better forecasting performance than many other artificial neural networks. The long short-term memory (LSTM) is one of the deep artificial neural networks. There have been a few fuzzy time series forecasting model based on LSTM in the literature. However, LSTM has not been used in an intuitionistic fuzzy time series (IFTS) forecasting method until now. In this paper, determining the fuzzy relations is made by using the LSTM artificial neural network and so, a new intuitionistic fuzzy time series forecasting method based on LSTM is proposed. In the proposed method, obtaining the membership and non-membership values is performed by using intuitionistic fuzzy c-means. Then, the inputs of the LSTM are merged membership and non-membership values by a minimum operator. In this way, lagged crisp values are inputs of the long short-term memory. So, the proposed method is a high-order IFTS model. The architecture of the LSTM artificial neural network includes multiple inputs and a single output. The proposed method and some other methods in the literature are applied to the Giresun Temperature data and the Nikkei 225 stock exchange time series, and the forecasting performance of these methods is compared. Keyword Intuitionistic fuzzy time series · Long short-term memory · Intuitionistic fuzzy c-means · Deep learning
* Cem Kocak [email protected] Erol Egrioglu [email protected] Eren Bas [email protected] 1
Department of Nursing, Faculty of Health Sciences, Hitit University, Çorum, Turkey
2
Department of Statistics, Faculty of Arts and Science, Giresun University, Giresun, Turkey
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1 Introduction In series analysis, classical time series methods like autoregressive integrated moving average (ARIMA), Holt’s exponential smoothing and Winter’s exponential smoothing [1] have been continued to use in the literature. Furthermore, the fuzzy time series (FTS) forecasting models have been proposed in the literature for a long time. FTS models do not require to have some statistical assumptions like the normality, the stability and the reversibility although these assumptions are needed in the classical time series approach. Also, FTS methods can have better forecasting performance than classical time series methods for much of reallife time series. Solving a fuzzy time series generally comprises of three stages called as the fuzzification, the determining of fuzzy relations and the defuzzification, respectively [2, 3]. 1.1 Literature review The first proposed FTS approach in the literature is the method of Song and Chissom [2] based on complex matrix operation calculations in determining fuzzy relations. Then, Chen [4, 5] proposed two FTS forecasting models that one of the
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