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

• Main Authors: Rozaimi Zakaria, Abd. Fatah Wahab, Isfarita Ismail, Mohammad Izat Emir Zulkifly
• Format: Article
• Language: English; English
• Published: Multidisciplinary Digital Publishing Institute (MDPI) 2021
• Subjects: QA1-939 Mathematics
• Online Access: https://eprints.ums.edu.my/id/eprint/34595/1/ABSTRACT.pdf; https://eprints.ums.edu.my/id/eprint/34595/2/FULLTEXT.pdf; https://eprints.ums.edu.my/id/eprint/34595/; https://www.mdpi.com/2227-7390/9/9/1054; https:// doi.org/10.3390/math9091054

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.