Neutrosophic Type Reduction for Type-2 Neutrosophic B-spline Curve Mode
DOI:
https://doi.org/10.11113/mjfas.v21n5.4313Keywords:
Type-2 Neutrosophic Set Theory, Neutrosophic Type Reduction, B-spline Curve Model, Approximation Method, Enhanced Liu and Karnik Mendel AlgorithmAbstract
The neutrosophic type reduction process converts type-2 neutrosophic values into their type-1 counterparts. Type-2 neutrosophic set (T2NS) theory is a comprehensive framework that encompasses intuitionistic fuzzy sets (IFS), fuzzy sets (FS), type-2 fuzzy sets (T2FS), and neutrosophic sets (NS). Within this framework, a T2NS employs six membership functions—truth, indeterminacy, and falsity- each represented with both primary and secondary values. The reduction process simplifies these memberships into a type-1 neutrosophic set (NS), which consists solely of the primary truth, indeterminacy, and falsity memberships. However, generating a geometric representation, such as a B-spline curve, presents challenges when using the T2NS theory due to the complexity involved in the reduction process. Therefore, this study introduces an enhanced type reduction technique inspired by the T2FS framework. The method employs the Liu and Karnik-Mendel algorithms to transform type-2 neutrosophic B-spline curves (T2NBsCs) into type-1 neutrosophic B-spline curves (T1NBsCs) for approximation. To construct the model, the triangular T2NS concept is utilized to define a type-2 neutrosophic control point relationship (T2NCPR), which is subsequently integrated with the B-spline basis functions. This integration produces T2NBsCs through an approximation process. The study then presents several numerical examples of T2NBsCs and illustrates the resulting T1NBsCs models along with the corresponding algorithm.”
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