Handling Forecasting Problems Based on Combining High-Order Time-Variant Fuzzy Relationship Groups and Particle Swam Optimization Technique

Abstract

Numerous fuzzy time series (FTS) forecasting methods have been proposed in scientific literature and has achieved growing attention in practice. Most of them are based on modeling fuzzy relationships(FRs) of the past data. In this paper, a new hybrid forecasting model based on the concept of time-variant FR group (TV-FRG), particle swarm optimization technique (PSO) and refinement technique in the defuzzization stage is presented to forecast the enrolments of the University and the stock market. PSO technique is utilized to adjust for obtaining the effective length of each interval in the universe of discourse for the forecasting model. Most of the existing forecasting models simply ignore the repeated FRs without any proper justification or accept the number of recurrence of the FRs without considering the appearance history of these FRs in the grouping FRs process. Therefore, the appearance history of the fuzzy sets on the right-hand side of the FRs is considered to establish the FR groups, called the TV-FRGs. Furthermore, the high-order TV-FRGs are used in order to obtain more accurate forecasting results in the defuzzication stage. To calculate these high-order TV-FRGs values, a refined defuzzication technique is developed, and incorporated in the proposed model. To verify the effectiveness of the proposed model, two numerical simulations are examined with the case of University enrollments and Taiwan futures exchange (TAIFEX). The experimental results show that the proposed model achieves good forecasting results compared to other existing forecasting models based on the high-order FTS. These promising results bring a significant meaning for the future work on the development of FTS and PSO algorithm in real-world forecasting applications.