Generation of Picture Fuzzy B-Spline Curve Interpolation with Open Uniform Knot Vector

Abstract

An open uniform knot vector ensures that the resulting B-spline curve starts at the first control point and ends at the last control points, providing a more intuitive and predictable shape at the boundaries. When dealing uncertainty in data, open uniform knot vector B-spline are particularly useful because they offer several advantages. In this paper, the picture fuzzy set approach was used to introduce the picture fuzzy B-spline curve interpolation model with open uniform knot vector. Firstly, picture fuzzy control point relation is introduced by using basic concepts of picture fuzzy set which is involved picture fuzzy number and picture fuzzy relation. The B-spline basis function is then blended with open uniform knot vector with order  and the picture fuzzy control point relation. Afterwards, using interpolation technique, fuzzy B-spline curves interpolation are generated and visualized using open uniform knot vector. In conclusion, a few numerical examples for creating the desired curve are displayed.