Probabilistic Fuzzy Time Series Forecasting Method Based on Cumulative Probability Based Discretization Approach and Particle Swarm Optimization

• Published in: SN computer science Vol. 6; no. 7; p. 759
• Main Authors: Gupta, Krishna Kumar, Saxena, Suneet
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01.10.2025; Springer Nature B.V
• Subjects: Accuracy; Algorithms; Computer Imaging; Computer Science; Computer Systems Organization and Communication Networks; Data Structures and Information Theory; Discretization; Distribution functions; Forecasting; Fuzzy logic; Fuzzy sets; Information Systems and Communication Service; Methods; Neural networks; Normal distribution; Optimization; Original Research; Particle swarm optimization; Pattern Recognition and Graphics; Probability; Probability distribution functions; Probability theory; Random variables; Randomness; Software Engineering/Programming and Operating Systems; Statistical analysis; Stock exchanges; Time series; Uncertainty; Vision; Probabilistic fuzzy logical relation; Uncertainties; Probabilistic fuzzy set; Particle swarm optimization
• ISSN: 2661-8907; 2662-995X; 2661-8907
• DOI: 10.1007/s42979-025-04292-8

Uncertainties in the system are likely not to be handled simultaneously due to randomness and fuzziness whereas probabilistic fuzzy set has been proved by the researchers to model such kind of uncertainties in different domains. In this paper, we propose a cumulative probability based discretization and particle swarm optimization based probabilistic fuzzy time series forecasting method. Gaussian probability distribution function has been used to evaluate the probabilities and associates to membership grades then constructed probabilistic fuzzy set. Advantage of the proposed work is that it may handle the uncertainties due to randomness and fuzziness in a single framework, it also improves accuracy rate in time series forecasting. Particle swarm optimization used to optimize the length of intervals which are obtained by cumulative probability based discretization approach and probabilistic fuzzy set can handle both kinds of uncertainties stochastic and non-stochastic simultaneously. In proposed forecasting method, we are also using an aggregation operator to aggregate probabilistic fuzzy outputs to fuzzy row vector. Proposed forecasting method is applied on time series data set of enrolments of University of Alabama and two financial datasets of State Bank of India share prices at Bombay Stock Exchange, India and Taiwan Stock Exchange Capitalization Weighted Stock Index. Out performance of proposed forecasting method based on probabilistic fuzzy set and particle swarm optimization is verify by using root mean square error, mean absolute deviation, tracking signal and evaluation parameter.