B-spline model based on Pythagorean fuzzy approach to handle uncertainty in ocean wave datasets
摘要
Ocean wave research is vital for maritime engineering, offshore operations, and coastal management, where accurate prediction and analysis are critical to ensuring safety and operational efficiency. However, uncertainty in ocean wave datasets presents a significant challenge. Traditional approaches such as fuzzy sets, type-2 fuzzy sets, and intuitionistic fuzzy sets (IFS) address data imprecision but struggle with hesitancy and incompleteness. IFSs, in particular, become invalid when the sum of membership and non-membership degrees exceeds one. To overcome these limitations, this study proposes a novel approach based on the Pythagorean fuzzy set (PFS) framework, which models both uncertainty and indeterminacy while relaxing the restrictive sum constraint of IFSs. A B-spline model is integrated into the PFS framework to construct a Pythagorean fuzzy B-spline for geometric modeling and wave pattern visualization. The B-spline is selected for its smoothness, local control, and adaptability to complex wave geometries, facilitating clear and precise visualization of irregular fluctuations. To support this integration, Pythagorean fuzzy control points are defined, and triangular Pythagorean fuzzy numbers are introduced for more effective representation of imprecise data. The proposed method is validated using ocean wave data from the Oregon coast, achieving 97.29% accuracy and statistical significance at the 90% confidence level based on the Wilcoxon signed-rank test. This integrated approach enhances modeling precision and provides deeper insights into wave behavior, supporting more informed decision-making in maritime and coastal applications.