This paper discusses the construction of a type-2 fuzzy B-spline model to model complex uncertainty of surface data. To construct this model, the type-2 fuzzy set theory, which includes type-2 fuzzy number concepts and type-2 fuzzy relation, is used to define the complex uncertainty of surface data in type-2 fuzzy data/control points. These type-2 fuzzy data/control points are blended with the B-spline surface function to produce the proposed model, which can be visualized and analyzed further. Various processes, namely fuzzification, type-reduction and defuzzification are defined to achieve a crisp, type-2 fuzzy B-spline surface, representing uncertainty complex surface data. This paper ends with a numerical example of terrain modeling, which shows the effectiveness of handling the uncertainty complex data.

Dealing with the uncertainty data problem using neutrosophic data is difficult since certain data are wasted due to noise. To address this issue, this work proposes a neutrosophic set (NS) strategy for interpolating the B-spline surface. The purpose of this study is to visualize the neutrosophic bicubic B-spline surface (NBB-sS) interpolation model. Thus, the principal results of this study introduce the NBB-sS interpolation method for neutrosophic data based on the NS notion. The neutrosophic control net relation (NCNR) is specified first using the NS notion. The B-spline basis function is then coupled to the NCNR to produce the NBB-sS. This surface is then displayed using an interpolation method that comprises surfaces representing truth, indeterminacy, and false membership. There is a numerical example for constructing the NBB-sS using interpolation and will use quantitative data in the form of discrete numerical cases, particularly in neutrosophic numbers. The major conclusion of this study is a mathematical representation of NBB-sS by using the interpolation method was introduced and visualized for a neutrosophic data problem. The scientific value contributed to this study is an acceptance of uncertainty. Therefore, since it incorporates geometric modeling, this work can make a significant contribution to the neutrosophic decision model.

Complex data is defined as data that has the qualities of huge data, a lack of data information, and uncertainty. This paper discussed constructing the interval neutrosophic cubic Bézier curve (INCBC) approximation model for complex data. To construct the interval neutrosophic data point (INDP) based on the definition of interval neutrosophic set (INS), interval neutrosophic relation (INR) and interval neutrosophic point (INP). Next is the introduction of an interval neutrosophic control point (INCP) that blends with the theory of interval neutrosophic set and the Bernstein basis function. Later, the interval neutrosophic cubic Bézier curve (INCBC) model is visualizing with a four-by-four control points relation approximates the curves for truth, false, and indeterminacy membership. At the end of this paper will demonstrate the algorithm for the creation of the interval neutrosophic cubic Bézier curve (INCBC). The scientific value of this work is the acceptance of complex uncertainty data. As a result, due to the fact it combines fuzzy geometric modelling, this approach has the potential to make a significant contribution to complex uncertainty modelling by using this spline which is Bézier curve model.

Surfaces and their descriptions are significant in design, physical science, geology, and other natural phenomena. This study introduces a neutrosophic B´ezier surface approximation with a four-by-four control net for the bicubic situation. The neutrosophic notion defines the neutrosophic control net relation. The control net is mixed with the Bernstein basis function to generate a surface blending function and a neutrosophic bicubic B´ezier surface. Finally, the neutrosophic bicubic B´ezier surface is shown using an approximation approach and data points having neutrosophic properties.

This study introduces a B-spline curve interpolation model based on the neutrosophic set technique. To begin, the neutrosophic notion is used to define the neutrosophic control point relation. After that, the neutrosophic control point is combined with the B-spline basis function. Besides, the neutrosophic B-spline curve interpolation model is illustrated using the interpolation method. Furthermore, an example and the methods are shown for creating the right curve.

In a 3-dimensional data collection process, there exists noise data that cannot be included to visualize the process. Therefore, it is difficult to deal with since fuzzy set and intuitionistic fuzzy set theories did not consider the indeterminacy problem. However, using a neutrosophic approach with three memberships: truth, false, and indeterminacy membership function, the error data will be treated as uncertain data by using the indeterminacy degree. Thus, this study will visualize the 3-dimensional quartic Bézier curve model by using neutrosophic set theory. To construct the model, the neutrosophic quartic control point must first be introduced to approximate the neutrosophic quartic Bézier curve. Next, the Bernstein basis function as the methodology of this study will be blended with the neutrosophic fundamental notion. At the end of this paper, a numerical example of the 3-dimensional neutrosophic quartic Bézier curve will be visualized by using the approximation method as the finding of this study. Finally, this study provides significant contributions to making it easier for data collectors to visualize all data, which means that no data will be eliminated since the uncertainty data will also be used.