Implementing 3D Modeling: Interpolated B-Spline Surfaces Enhanced with Interval Type-2 Neutrosophic Set Theory

Abstract

The interval type-2 neutrosophic set (IT2NS) is a superset of the type-1 neutrosophic set, interval type-2 fuzzy set, and intuitionistic fuzzy set.  This paper will demonstrate how to use the interpolation strategy to depict the interval type-2 neutrosophic B-spline surface (IT2NB-sS) model. However, the presence of truth, indeterminacy, and falsity membership functions in neutrosophic features makes the model difficult to visualize. Aside from that, IT2NS properties have upper and lower bounds that make them challenging. This study will use the IT2NS theory to develop the model by introducing an interval type-2 neutrosophic control net relation (IT2NCNR). The IT2NB-sS models will be represented by combining the IT2NCNR with the B-spline basis function. The IT2NCNR's truth, indeterminacy, and falsity memberships are then interpolated for upper and lower bounds to reveal the IT2NB-sSs. The study will conclude by reviewing the algorithm used to construct the IT2NB-sS interpolation models. As a result, the study's findings will result in a prediction model that may be used in various data-gathering applications, including medical applications and real-world data such as bathymetry that involve uncertainty problems.