Abstract
A time series is a sequence of observations that a variable takes with respect to times. It has a wide range of applications in decision making and forecasting in economics, agriculture, medicine, industry, energy sector and other scientific fields. Time series modeling and forecasting contain some of the classical issues that are widely addressed in the literature based on traditional statistical models with low interpretability. Fuzzy time series has become a powerful tool that can counter the problem of prediction of historical data in linguistic terms. This study proposes a new framework for modeling the fuzzy time series approach in the environment of intuitionistic fuzzy set theory to play viable role in ensuring robustness to the uncertainty involved in data series. In order to get the optimized length of intervals, the principles of fuzzy c-means (FCM) clustering and information granules are integrated. To fuzzify the historical data, intuitionistic fuzzy triangular function is practiced to acquire the intuitionistic fuzzy sets. Furthermore, the distance measures between the elements of the intuitionistic fuzzy set of the fuzzified historical data and the centers of the corresponding clusters are computed for all fuzzy sets. Finally, a robust fuzzy time series model is designed by extracting fuzzy logical relationships and employing weighted association reasoning as an exhaustive defuzzification approach. The parameters of accuracy measures such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) are used to identify the strength of the proposed modeling and forecasting. Findings demonstrate that the proposed forecasting method is robust in determining the highly accurate forecasts.
Highlights
In practice of time series modeling and forecasting, classical issues are widely addressed in literature by data analysts from almost every domain, e.g., capital planning, scientific experiments, stock management information, biological and medical experiments, miscellaneous findings from sensorThe associate editor coordinating the review of this manuscript and approving it for publication was Dazhong Ma .system and different data sets regarding quality parameters
Let an intuitionistic fuzzy set is denoted by Ã, which characterizes the both membership ui and non-membership vi information, Intuitionistic fuzzy triangular function (IFTF) is described by three parameters, a lower bound α, an upper bound c, and a value b, such that α ≤ b ≤ c
Definition 5. suppose there are fuzzy logical relationships groups (FLRGs) such that Fi −→ Fj1, Fi −→ Fj2, . . . Fi −→ Fjn, these relationships can be grouped as Fi −→ Fj1Fj2, . . . Fjn
Summary
In practice of time series modeling and forecasting, classical issues are widely addressed in literature by data analysts from almost every domain, e.g., capital planning, scientific experiments, stock management information, biological and medical experiments, miscellaneous findings from sensor. The concept of intuitionistic fuzzy sets (IFSs) was delivered by [35] to tackle the issue of non-determinism as an extension of Zadeh’s work [2] This capable theory has attracted the researchers for forecasting and decision-making problems [36]–[38]. There are some drawbacks about consideration of weights properly, which effect the accuracy of forecasting To address this issue, this study proposes a unique weighted association approach, which utilize the membership function and the additional information of non-membership information to build the model for one and more than one fuzzy logical relationships (FLRs). The significance of this study is to design a robust forecasting algorithm that have capability to combat the problems of uncertainty and vagueness in historical data by optimize partitioning and proper utilization of membership information to overcome the prediction process obstruction.
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