Statistical Control Points: Approximate Methods for Solving First Order Fuzzy Initial Value Problems

Abstract

This article proposes two approximate methods for solving first order Fuzzy Initial Value Problems (FIVPs) using new forms of Bezier curves and B-Spline control point’s techniques. Fuzzy set theory principles and characteristics are utilized to update and evaluate the suggested techniques for solving both linear and nonlinear fuzzy problems. The control points on the Bezier curve are determined by minimizing the residual function using the least square method. This ensures that the curve approximates the solution to the FIVP. The Bezier curve is a mathematical curve commonly used in computer graphics and geometric modelling. Furthermore, B-Spline interpolation techniques are employed to enhance the accuracy of the solution. B-Splines are a type of mathematical spline function that allows for smooth and flexible interpolation of data points. The article presents numerical examples to illustrate the effectiveness of the proposed method. A comparison is made between the obtained results and the exact solution to demonstrate the capabilities of the method in accurately solving FIVPs. Overall, the article introduces a novel approach to solving first order fuzzy initial value problems. By utilizing Bezier curves, B-Spline interpolation techniques, and principles from fuzzy set theory, the method aims to provide accurate and efficient solutions. The numerical examples serve as evidence of the method's effectiveness in practice. © 2026 NSP Natural Sciences Publishing Cor.