Abstract: In time series prediction tasks, the uncertainty of historical observations poses difficulties in forecasting. However, the forecasting methods based on fuzzy time series have unique advantages in dealing with data uncertainty. Probabilistic forecasting, on the other hand, can provide the distribution of the predicted target and quantify the uncertainty of the prediction results. Therefore, a fuzzy time series probabilistic forecasting method based on a probability weighting strategy is proposed to reduce the impact of uncertainty on the forecasting task. The proposed method builds a probability-weighted fuzzy time series prediction model using historical observations of the target variable, and refines the fuzzy rule base of the prediction model by introducing additional observations. Specifically, two operators with low computational cost are used to reconstruct the fuzzy logic relationships. The intersection operator is used to exclude the interfering information, while the union operator merges all information, resulting in two different sets of fuzzy logic relationship groups. The relationship group corresponding to the current observation value in two sets is the prediction for the fuzzy set in the next moment. Finally, the probability distribution of the next moment is output by defuzzification. Experimental results on publicly available time series data sets verify the accuracy and validity of this method, and the prediction accuracy is remarkably improved in comparison to the newly proposed PWFTS prediction method.

Key words: fuzzy time series, probabilistic forecasting, fuzzy logical relationship, intersection operator, union operator