K-Means Clustering Based High Order Weighted Probabilistic Fuzzy Time Series Forecasting Method

In the present study, we propose a novel high-order weighted fuzzy time series (FTS) forecasting method using k-mean clustering, weighted fuzzy logical relations and probabilistic fuzzy set (PFS). Objective of proposed forecasting method is to handle occurrence of recurrence of fuzzy logical relations and both non-probabilistic and probabilistic uncertainties in assigning membership grades to time series datum. The proposed PFS-based forecasting method uses Gaussian probability distribution function to assign probabilities to membership grades. Proposed FTS forecasting method uses high-order weighted fuzzy logical relation in which each fuzzy logical relation uses the weight in ascending order. Superiority of proposed method is shown by implementing it on SBI share price at BSE, India and University of Alabama enrollments. Error measures and statistical parameters, for example, coefficient of correlation, coefficient of determination, performance parameter, evaluation parameter and tracking signal are also used to confirm the outperformance and validity of the proposed PFS-based forecasting method.