Probabilistic fuzzy set (PFS) is an ideal tool to touch uncertainties due to randomness (probabilistic) and fuzziness (non-probabilistic) in a single framework. In the present study, we divide time series data into clusters and propose a novel weighted fuzzy time series (FTS) forecasting method using PFS. Proposed method models non-probabilistic uncertainty due to imprecision and linguistic representation of time series data and probabilistic uncertainties in assigning membership grades to time series datum along with occurrence of recurrence of fuzzy logical relations. In proposed forecasting method, probabilities to membership grades are assigned using Gaussian probability distribution function (PDF). Time series data of SBI share price are forecasted using proposed forecasting method in order to show its suitability and applicability. Root mean square error and average forecasting error are used as performance indicator to confirm the outperformance of proposed weighted fuzzy time series forecasting method based on PFS.

In the literature of time series forecasting, no method can handle both probabilistic and non-probabilistic uncertainty simultaneously. In the current investigation, we have presented probabilistic fuzzy set (PFS) based fuzzy time series (FTS) forecasting model to describe the issue of uncertainties that rises due to randomness as well as linguistic representation of time series data. An aggregation operator is also presented in this paper to aggregate the fuzzified outputs using with membership grades associated with corresponding probabilities. The presented model has been applied to forecast the time series data of University of Alabama enrolments. The performance of presented model has been examined in terms of RMSE and AFE.