Type-2 Fuzzy Interpolation Bezier Curve Model for Earthquake Magnitude Uncertainty Data Modeling

Abstract

Uncertainty is a fundamental characteristic of real-world data, especially in the modeling of curves and surfaces, where variability can be intricate and challenging to accurately represent. Conventional modeling methods, dependent on static numerical representations, often struggle to deliver a dependable characterization of uncertainty, leading to diminished accuracy and restricted interpretability. This study examines the issue of insufficient representation of complex uncertainty in data modeling, emphasizing the necessity for methodologies that can incorporate variability while maintaining critical structural information. This research aims to present a more advanced framework for uncertainty modeling by utilizing type-2 fuzzy numbers (T2FN), which provide enhanced capabilities for characterizing imprecision in comparison to traditional methods. The proposed method utilizes a Type-2 fuzzy interpolation Bezier curve (T2FIBC), facilitating the visualization of uncertainty while effectively capturing the underlying data trends. The model leverages the descriptive capabilities of type-2 fuzzy sets, offering a more nuanced and adaptable representation of uncertainty. Experimental results indicate that the T2FIBC approach attains superior accuracy and robustness compared to conventional interpolation techniques, especially in situations characterized by considerable variability. The model further improves the visualization of uncertainty, providing more precise insights into the behavior of intricate datasets. In conclusion, this research validates the effectiveness of Type-2 fuzzy interpolation Bézier curves as a significant asset for addressing uncertainty in data modeling. This approach not only enhances the analysis of geoscientific datasets, including earthquake magnitude records, but also offers a versatile framework applicable to various fields where effective representation of uncertainty is crucial for reliable decision-making.