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.

The solution of a problem that involves uncertainty data that is characterized by complex process in which the phenomenon of incomplete information obtained is difficult to handle. Various mathematical models have been developed to handle problems involving uncertainty data. This paper introduced new concept of geometric modeling with intuitionistic fuzzy called intuitionistic fuzzy Bezier model. This model is constructed through intuitionistic fuzzy set theory and based on intuitionistic fuzzy number and intuitionistic fuzzy relation. A new control point namely intuitionistic fuzzy control point is defined. Next, the new control point is blended with the spline basis function to developed intuitionistic fuzzy Bezier model and the curve is shaped.

Surface and their description plays an important role in design, physical, geology and other natural phenomenon. In this paper, intuitionistic fuzzy Bézier surface approximation that considers bicubic case with 4×4 control net is introduced. The intuitionistic fuzzy control net relation is defined through intuitionistic fuzzy concept. Later, the control net is blended with Bernstein basis function to obtain surface blending function and to produce intuitionistic fuzzy bicubic Bézier surface. Lastly, the intuitionistic fuzzy bicubic Bézier surface is illustrated through the approximation method by using data point with intuitionistic features.

A fuzzy linguistic data set that is uncertain is difficult to analyze and describe in the form of a smooth and continuous generic figure. Therefore, the study aims to develop a new model of a B-spline surface using a different approach of a crisp and fuzzy linguistic point relation with three types of linguistic function: low $L$, medium $M_i$ and high $H$. These linguistic functions are defined first to introduce the fuzzy linguistic point relation. Then, a new algorithm of the fuzzy linguistic bicubic B-spline surface model is presented to convert fuzzy linguistic data into fuzzy linguistic control points. In addition, a numerical example of fuzzy linguistic data is considered at the end of this study to visualize the suggested model. Thus, the relation between the fuzzy linguistic data points can be analyzed to present another area of knowledge in which symmetry phenomena occur. The symmetry here plays an important role in solving the uncertain fuzzy linguistic data problem by using the suggested model.

In this paper, the cubic Bézier curve interpolation method for intuitionistic fuzzy data is introduced based on the theory of intuitionistic fuzzy sets. The intuitionistic fuzzy point relation and intuitionistic fuzzy control point relation is defined based on intuitionistic fuzzy point, intuitionistic fuzzy number and intuitionistic fuzzy relation concepts. Next, the intuitionistic fuzzy control point relation is blended with the Bernstein basis function and the intuitionistic fuzzy cubic Bézier curve is produced. Then, the intuitionistic fuzzy data is interpolated and visualized by using the intuitionistic fuzzy cubic Bézier curve.