Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model

Rozaimi Zakaria, Abd. Fatah Wahab, Isfarita Ismail and Mohammad Izat Emir Zulkifly
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Rozaimi Zakaria: Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Jalan UMS, Sabah 88400, Malaysia
Abd. Fatah Wahab: Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu 21030, Malaysia
Isfarita Ismail: Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Jalan UMS, Sabah 88400, Malaysia
Mohammad Izat Emir Zulkifly: Faculty of Science, Universiti Teknologi Malaysia, Skudai, Johor Bahru, Johor 81310, Malaysia

Mathematics, 2021, vol. 9, issue 9, 1-18

Abstract: 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.

Keywords: type-2 fuzzy set; fuzzification; type-reduction; defuzzification; B-spline surface model function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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