A Novel Hybrid EMPSO-PFTS Method for Fuzzy Time Series Forecasting: Integrating Picture Fuzzy Sets and Exponentially Mutated Particle Swarm Optimization

Abstract

Current research has demonstrated that fuzzy sets can be used to address forecasting issues. Researchers have created numerous fuzzy time series (FTS) approaches without taking into account the non-determinacy. For a considerable period, researchers have consistently focused on two significant key issues: determining the optimal interval size and incorporating non-determinacy. The focus of this article is to present a groundbreaking picture fuzzy time series (PFTS) forecasting model that is constructed based on the principles of picture fuzzy sets (PFSs). A PFS represents a generalized form of fuzzy and intuitionistic fuzzy sets. Here picture fuzzy clustering (PFC) technique is utilized for the construction of PFS. In this article, we integrate PFS and exponentially mutated particle swarm optimization (EMPSO) to develop a novel hybrid EMPSO-PFTS forecasting method. Optimal length is determined by EMPSO, and non-determinacy is taken into account by PFS when time series data is fuzzy. The suggested forecasting method is used on data sets from the University of Alabama and the market price of the State Bank of India (SBI-P) at the Bombay Stock Exchange, India, to demonstrate its applicability and usefulness. Mean square error (MSE) and average forecasting error (AFE) are used to gauge the effectiveness of the proposed method. The significant reduction in both MSE and AFE is strong evidence of the superior performance of the proposed EMPSO-PFTS method compared to various existing methods. To ensure the reliability and validity of the proposed method, rigorous statistical validation and performance analysis are conducted.