Complex uncertainty of surface data modeling via the type-2 fuzzy b-spline model

• Main Authors: Zakaria, R., Wahab, A. F., Ismail, I., Zulkifly, M. I. E.
• Format: Article
• Language: English
• Published: MDPI AG 2021
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/95154/1/MohammadIzatEmir2021_ComplexUncertaintyofSurface.pdf; http://eprints.utm.my/id/eprint/95154/; http://dx.doi.org/10.3390/math9091054
• Institution: Universiti Teknologi Malaysia

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.