3-tuple Bézier surface interpolation model for data visualization

In this paper, the 3-tuple Bézier surface interpolation model is introduced. The 3-tuple 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 3-tuple Bézier surface. The 3-tuple Bézier surface model is illustrated through the interpolation method by using data point with intuitionistic features. Some numerical example is shown. Lastly, the 3-tuple Bézier surface properties is also discussed

An Estimation of Underground Economy in Afghanistan Using Mathematical Fuzzy Model Based on Mean and Standard Deviation

The underground economy (UE) briefly comprises services, activities, and transactions, which could be legal or illegal. In this paper the size of UE is estimated through mathematical fuzzy model based on fuzzy set, fuzzy logic and constructed a yearly time-series for UE over the period 2001 to 2020 in Afghanistan. Two input variables are used; unemployment rate (UR) and the government regulations (REG). Fuzzification, fuzzy inference and defuzzification; the three steps that are considered for estimating UE in the country, based on mean and standard deviation (SD) for each variable individually. The result indicates four cycles for time series and shows that people were more involved in UE activities over the first and third cycles and less involved over the second and fourth cycles

B-spline curve interpolation model by using intuitionistic fuzzy approach

In this paper, B-spline curve interpolation model by using intuitionistic fuzzy set approach is introduced. Firstly, intuitionistic fuzzy control point relation is defined based on the intuitionistic fuzzy concept. Later, the intuitionistic fuzzy control point relation is blended with B-spline basis function. Through interpolation method, intuitionistic fuzzy B-spline curve model is visualized. Finally, some numerical examples and an algorithm to generate the desired curve is shown

B-spline curve interpolation model by using intuitionistic fuzzy approach

In this paper, B-spline curve interpolation model by using intuitionistic fuzzy set approach is introduced. Firstly, intuitionistic fuzzy control point relation is defined based on the intuitionistic fuzzy concept. Later, the intuitionistic fuzzy control point relation is blended with B-spline basis function. Through interpolation method, intuitionistic fuzzy B-spline curve model is visualized. Finally, some numerical examples and an algorithm to generate the desired curve is shown

B-spline curve interpolation model by using intuitionistic fuzzy approach

In this paper, B-spline curve interpolation model by using intuitionistic fuzzy set approach is introduced. Firstly, intuitionistic fuzzy control point relation is defined based on the intuitionistic fuzzy concept. Later, the intuitionistic fuzzy control point relation is blended with B-spline basis function. Through interpolation method, intuitionistic fuzzy B-spline curve model is visualized. Finally, some numerical examples and an algorithm to generate the desired curve is shown

Fuzzy Bézier curve interpolation modeling by using fuzzy control point relation

Based on the theory and concept of fuzzy point relation, we introduce fuzzy Bézier curve interpolation and derive some of its properties. Based on this notion, fuzzy control point relation is defined which is then blended with the Bernstein basis function to generate fuzzy Bézier curve by using interpolation method. An algorithm to obtain fuzzy Bézier curve interpolation is provided at the end of this paper

Development of non-uniform rational type-2 fuzzy B-spline curve modeling

Type-2 fuzzy set offers an opportunity to define a fuzzy control point with type-2 levels of uncertainty. We discuss the development of non-uniform B-spline curve model based on type-2 fuzzy set theory and also a type-2 level of NURBS curve model. First we define type-2 fuzzy control points and type-2 fuzzy weight using a type-2 fuzzy number. Then we introduce fuzzy NURBS curve model with type-2 fuzzy control points and type-2 fuzzy weight. We discuss the model with type-2 fuzzy data points and type-1 fuzzy reduction. The defuzzification of the model is also discussed at the end of this paper

Generalized Fuzzy Linguistic Bicubic B-Spline Surface Model for Uncertain Fuzzy Linguistic Data

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 Mi 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

Generalized fuzzy linguistic cubic B-spline curve model for uncertainty fuzzy linguistic data

Fuzzy linguistic data is difficult to analyze. It becomes a problem to describe the data in the form of smooth and continuous generic figure. Therefore, the generalization of the problems of linguistic data in the form of curves and surfaces requires a new model such as fuzzy linguistic B-spline by using fuzzy linguistic approach. This paper discusses an approach of fuzzy linguistic point relation with three types of linguistic functions that generate new B-spline curve model

Generalized Fuzzy Linguistic Bicubic B-Spline Surface Model for Uncertain Fuzzy Linguistic Data

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 Mi 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