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.
A new types of spline modeling using fuzzy linguistic approach AIP Conference Proceedings 1750, 020020 (2016) Abstract. The solution of a problem that involves uncertainty data that is characterized by complex process in which the phenomenon of incomplete information obtained is difficult to handle. Various mathematical models have been developed to handle problems involving uncertainty data. This paper introduced new concept of geometric modeling with intuitionistic fuzzy called intuitionistic fuzzy Bezier model. This model is constructed through intuitionistic fuzzy set theory and based on intuitionistic fuzzy number and intuitionistic fuzzy relation. A new control point namely intuitionistic fuzzy control point is defined. Next, the new control point is blended with the spline basis function to developed intuitionistic fuzzy Bezier model and the curve is shaped.
Underground economy (UE) is known as hidden economy or shadow economy referring to unpaid tax. We applied interval type-2 fuzzy logic system (IT2 FLS) model in measuring the index value (IV) of UE in Malaysia over the period from 2001 to 2010. The efficiency of IT2 FLS model, the flow and trend of UE in Malaysia is discussed.
The uncertainty data problem with intuitionistic information is difficult to deal with through the methodology or approach available. This is because the existing fuzzy geometric modeling can only solve the fuzzy data problem that is intuitionistic and fuzzy complex in nature as the data have information that is incomplete boundary value (less clear and ambiguous), have meaning and truth value of the range, a lot of value logic values as well as having vague distribution and indistinct. Furthermore, the operation is characteristically minimum or maximum and image together with the range are obscure and complex. To solve this problem, a new model with a redefinition of the control points which characterized by three important components of intuitionistic fuzzy is developed. These control points will be blended with the basic functions of spline to generate several models in the form of intuitionistic fuzzy spline curve / surface and can be easily understood. With the intuitionistic concept and its relations, then the relevant data can be translated through the production of these models.
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