Picture Fuzzy Time Series Forecasting with a Novel Variant of Particle Swarm Optimization

Current research has demonstrated that fuzzy sets can be used to address forecasting issues. Researchers have created numerous fuzzy time series approaches without considering 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 ground breaking picture fuzzy time series forecasting model constructed based on the principles of picture fuzzy sets. Here picture fuzzy clustering technique is utilized for constructing picture fuzzy sets. This article presents a novel variant of particle swarm optimization (EDSPSO) algorithm, enhancing the particle swarm optimization algorithm with the exponential mutation operator and a dual-swarm strategy. This article integrates picture fuzzy set and EDSPSO to develop a novel hybrid EDSPSO–PFTS forecasting method. EDSPSO determines the optimal length, and non-determinacy is taken into account by picture fuzzy set when time series data is fuzzy. The suggested forecasting method is used on data sets from the University of Alabama and the share price of the State Bank of India at the Bombay Stock Exchange, to demonstrate its applicability and usefulness. Mean square error and average forecasting error are used to gauge the effectiveness of the proposed method. The significant reduction in both mean square error and average forecasting error serves as solid evidence of the superior performance of the proposed forecasting method compared to various existing methods. To ensure the reliability and validity of the proposed method, rigorous statistical validation and performance analysis are conducted.