Hesitant probabilistic fuzzy set based time series forecasting method

Uncertainties due to randomness and fuzziness coexist in the system simultaneously. Recently probabilistic fuzzy set has gained attention of researchers to handle both types of uncertainties simultaneously in a single framework. In this paper, we introduce hesitant probabilistic fuzzy sets in time series forecasting to address the issues of non-stochastic non-determinism along with both types of uncertainties and propose a hesitant probabilistic fuzzy set based time series forecasting method. We also propose an aggregation operator that uses membership grades, weights and immediate probability to aggregate hesitant probabilistic fuzzy elements to fuzzy elements. Advantages of the proposed forecasting method are that it includes both type of uncertainties and non-stochastic hesitation in a single framework and also enhance the accuracy in forecasted outputs. The proposed method has been implemented to forecast the historical enrolment student’s data at University of Alabama and share market prizes of State Bank of India (SBI) at Bombay stock exchange (BSE), India. The effectiveness of the proposed method has been examined and tested using error measures.