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Type-2 Fuzzy Bezier Surface
Rozaimi Zakaria, Abd Fatah Wahab
Abstract
In this paper, we proposed a new method in handling and modeling the complex uncertainty data points in surface form. The proposed method is the type-2 fuzzy Bezier surface(T2FBS) which is constructed by using the type-2 fuzzy set theory(T2FST) or more specifically type-2 fuzzy number(T2FN) concepts. T2FN is being used to define the complexity of uncertainty data as the data are the uncertainty values of real numbers. Therefore, type-2 fuzzy data/control point(T2FD/CP) is defined first before modeled the data through Bezier surface function, which develop T2FBS. After the data has been modeling, then we applied fuzzification process(alpha-cut operation) which reduces the fuzzy interval value. Later, we applied type-reduction method, which is used to reduce to become type-1 fuzzy Bezier surface(T1FBS) so that we can use the defuzzification method to obtain a crisp fuzzy solution of T2FBS. This defuzzification method is applied only to type-1 fuzzy cases and unsuitable for type-2 fuzzy cases unless it had been reduced to T1FBS. For more understanding, this paper shows some illustrations of T2FBS, and some algorithm are shows on the stage in defining complex uncertainty data to crisp fuzzy solution of T2FBS.
Keywords
Type-1 and type-2 fuzzy data/control points, type-1 and type-2 fuzzy Bezier surface, fuzzification, type-reduction, defuzzification.
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