A novel high-order fuzzy time series forecasting method based on probabilistic fuzzy sets

Recently, the probabilistic fuzzy set has been applied by the researchers in various domains to model the uncertainties in the system due to both fuzziness and randomness. In this research paper, we propose a novel high-order probabilistic fuzzy set-based forecasting method in the environment of both non-probabilistic and probabilistic uncertainties. We have also proposed a novel probability-based discretization approach to model probabilistic uncertainty during partitioning of time series data. Gaussian probability distribution function is used in this research paper to associate probabilities to membership grades and probabilistic fuzzy elements are aggregated to a fuzzy row vector using an aggregation operator. Major advantages of the proposed method are that it includes both types of uncertainties in a single framework and enhances accuracy in forecast as well. To show its suitability and outperformance over other existing forecasting methods, the proposed method is implemented in University of Alabama enrolments and TAIFEX time series datasets. Various statistical parameters, e.g., coefficient of correlation, coefficient of determination, performance parameter, evaluation parameter and tracking signal are used to verify the validity of proposed PFS-based high-order time series forecasting method.