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Top1. Introduction
The aim of forecasting is to predict a future value of a variable such as amount of rainfall, temperature, demand for a product, air quality index, interest rate, etc. (Jain & Kumar,2015). Forecasts drive a wide variety of business decisions, from sentiment analysis to long term forecasting (Jain & Kumar, 2016).The objective of forecasting is to determine what forecasting technique is the most suitable for what is being forecasted, and to maintain a strict regulation of reviewing forecasts(Jain & Kumar,2017).Various models are being used for time series forecasting like moving averages, integrated moving averages, regression analysis, autoregressive moving averages (Singh, 2008), but not all methods produce acceptable results, especially, when the data under consideration show significant turbulences. Turbulence, in this context, refers to sudden rises and dips in the time series data under consideration, for example, data set comprises of students’ enrollment in a university tends to be much less turbulent than a data set consists of stock exchange indices. To demonstrate the effectiveness of the proposed method, sales data of Tata Nano car in India from Jul-09 to Jan-12 are used. Pandey et al. (2013b) stated that various political, socio-political, technical, and promotional series of events might be the reason behind a turbulent sales pattern of the Tata Nano.
Zadeh (1965) introduced fuzzy set theory and fuzzy logic that offers a systematic method for handling ambiguities and uncertainties in data in linguistic terms. Fuzzy set theory is being used extensively in every area of engineering and sciences to tackle the problems caused by ambiguities in data. Time series forecasting is no exception; when fuzziness is incorporated in time series data to determine appropriate forecasts, it is called Fuzzy Time Series (FTS) forecasting.
The first recognized work in the area of FTS is attributed to Song and Chissom (1993, 1994) who developed FTS model to forecast the enrollment of the University of Alabama. Later, Chen (1996) contributed to the field of FTS forecasting by improving the work of Song and Chissom (1993,1994), where simple arithmetic operations were used in place of complex max-min operations discussed in Song and Chissom (1993,1994). Huarng (2001a) considered heuristic functions as a supplement to the knowledge base in FTS forecasting. Huarng (2001b) presented an approach based on interval length selection and assumed interval selection as a considerable parameter in FTS forecasting. Chen (2002) considered forecasting with high-order fuzzy time series models as a solution to non-deterministic states that arise during FTS forecasting. Other contributions to FTS forecasting are made by Singh (2007a), Singh (2007b) and Singh (2008) where a variety of time-variant difference parameters are used over the current state to forecast the next state. A number of modern researchers used advanced optimization techniques in fuzzy time series forecasting like the use of particle swarm optimization to get the optimal intervals in the universe of discourse (Chen & Kao, 2013) and membership values in the fuzzy relationships (Aladag et al., 2012).
In Table 1, we present a chronological survey of different FTS methods introduced over time with their authors, data set, method used and major focus. This survey is inherited and adapted from Pandey et al. (2013b).