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Abstract Fuzzy time series (FTS) forecasting models are widely applicable when the information is imprecise and vague. The concept of fuzzy set (FS) is generalized to intuitionistic fuzzy set (IFS) and proved that it is more suitable and powerful tool to deal with real life problems under uncertainty as compared to FSs theory. In this study, first we extended the definitions of FTS to the IFSs and proposed the notion of intuitionistic FTS. Further, the presented concept of intuitionistic FTS is applied to develop a forecasting model under uncertainty. Then, it is applied to the benchmark problem of the historical enrollments data of University of Alabama and the obtained results are compared with the results obtained by existing methods to show its effectiveness as compared to FTS. Keywords Fuzzy time series series


Intuitionistic fuzzy sets
Intuitionistic fuzzy time

1 Introduction The theory of FSs [1] is successfully implemented by Song and Chissom and developed the FTS models [2, 3], and applied it to the student enrollments of university of Alabama [3, 4]. A simplified method for time series forecasting by using the arithmetic operations is presented by Chen [5] and found the results of B.P. Joshi (&) Department of Applied Sciences, Seemant Institute of Technology, Pithoragarh, India e-mail: [email protected] Mukesh Pandey Department of Computer Science and Engineering, Seemant Institute of Technology, Pithoragarh, India e-mail: [email protected] Sanjay Kumar Department of Mathematics, Statistics & Computer Science, G.B. Pant University of Agriculture & Technology, Pantnagar, India e-mail: [email protected] © Springer Science+Business Media Singapore 2016 M. Pant et al. (eds.), Proceedings of Fifth International Conference on Soft Computing for Problem Solving, Advances in Intelligent Systems and Computing 436, DOI 10.1007/978-981-10-0448-3_70

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higher accuracy. In [6], Huarng introduced a heuristic model for FTS forecasting with the help of increasing and decreasing relations to enhance the forecasting results. A forecasting method based on high-order FTS was proposed in [7]. Lee and Chou [8] modified the Chen’s method [5] and improved the outputs. After that, many researchers [9–12] etc. did significant contribution in the theory of FTS. In [13], Atanassov extended the concept of FS, and defined the concept of IFS by incorporating the degree of uncertainty to FSs. The theory of IFS is more suitable and powerful tool to deal with real life problems under uncertainty and vagueness as compared to FSs theory. Due to the handling property of IFS with uncertainty Joshi and Kumar [14–16] proposed FTS forecasting model based on IFS. The forecasted values obtained under IFS [15] are close to the actual ones as compared to other forecasting methods, which show the effectiveness of incorporating IFSs to the FTS models. Thus, in this paper, the concept of intuitionistic FTS is proposed by studying the definitions of FTS presented by Song and Chissom. Based on the presented concept

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