A New Refined Forecasting Model Based on the High - Order Time-Variant Fuzzy Relationship Groups and Particle Swam Optimization

Abstract

In this paper, a novel refined fuzzy time series (FTS) model is presented to handle three main issues, viz., determination of effective length of intervals, handling of fuzzy logical relationships (FLRs) and determination of forecasted output values. In forecasting models, lengths of intervals always affect the results of forecasting. So, we use particle swarm optimization (PSO) technique to find the optimal length of intervals in the universe of discourse. Most of the existing forecasting models simply ignore the repeated FLRs without any proper justification or accept the number of recurrence of the FLRs without considering the appearance history of these fuzzy sets in the grouping fuzzy logical relationships process. Therefore, in this study, we consider the appearance history of the fuzzy sets on the right-hand side of the FLRs to establish the fuzzy logical relationship groups, called the time - variant fuzzy relationship groups (TV-FRGs). Furthermore, many researchers suggest that high-order FLRs improve the forecasting accuracy of the models. Therefore, we also use the high-order fuzzy relationships in order to obtain more accurate forecasting results. Proposed model is applied to forecast two numerical datasets (enrollments data of the University of Alabama, dataset of Gasonline Price in Viet Nam). The results indicate that the proposed model gets a higher average forecasting accuracy rate to forecast enrolments of the University of Alabama than the existing methods based on the high-order FTS.