Fuzzy Time Series Forecasting: Developing a new forecasting model based on high order fuzzy time series
Author
Poulsen, Jens Rúni
Term
4. term
Education
Publication year
2009
Pages
67
Abstract
Fuzzy Time Series (FTS) modeller forudsiger, hvordan værdier ændrer sig over tid, ved hjælp af fuzzy logik, som kan repræsentere usikkerhed. Højordens FTS-modeller—som ser flere tidsskridt tilbage—er ofte de mest nøjagtige, men de har tre grundlæggende udfordringer: Nøjagtigheden falder efter defuzzificering (når man omsætter fuzzy resultater til præcise tal), data udnyttes dårligere jo højere orden modellen har, og nøjagtigheden er følsom over for, hvordan dataintervallet opdeles. Denne afhandling introducerer en ny højordens FTS-model, der adresserer disse problemer. Modellen kombinerer aggregering med partikelsværmoptimering (PSO), en optimeringsmetode inspireret af flokadfærd, for at finjustere de enkelte prognoseregler og mindske afstanden mellem prognoser og faktiske værdier. I sammenlignende eksperimenter med metoder fra litteraturen opnåede modellen højere nøjagtighed. Fordi reglerne justeres individuelt, forbliver de defuzzificerede prognoser konsistente med de faktiske værdier, uanset hvordan intervalopdelingerne er valgt. Tilgangen forbedrer også dataudnyttelsen ved (1) at reducere tabet af prognoseregler og (2) at nedbringe antallet af mønsterkombinationer, der skal matches med fremtidige data. Som et biprodukt præsenterer afhandlingen en trapez-baseret fuzzificeringsalgoritme, der deler dataintervallet ("universe of discourse") objektivt uden behov for brugerdefinerede parametre.
Fuzzy Time Series (FTS) models forecast how values change over time using fuzzy logic, which represents uncertainty. High-order FTS models—those that look back multiple time steps—are often the most accurate, but they face three core issues: accuracy drops after defuzzification (turning fuzzy results into precise numbers), data is underused as model order increases, and accuracy is sensitive to how the data range is partitioned into intervals. This thesis presents a new high-order FTS model to address these challenges. The model combines aggregation with particle swarm optimization (PSO), an optimization method inspired by group movement, to fine-tune individual forecasting rules and reduce the gap between forecasts and actual outcomes. In comparative experiments against methods reported in the literature, the proposed model achieved higher accuracy. Because rules are tuned individually, defuzzified forecasts remain consistent with actual values across different interval partitions. The approach also improves data utilization by (1) reducing the loss of forecasting rules and (2) cutting down the number of pattern combinations that must be matched to future data. As a byproduct, the thesis introduces a trapezoid-based fuzzification algorithm that objectively partitions the data range (the “universe of discourse”) into intervals without requiring user-defined parameters.
[This abstract was generated with the help of AI]