Type-2 Fuzzy Curve Model

Abstract

The paper discusses about the formulation of type-2 fuzzy curve model. The generalization is carried out due to the existence of complex uncertainty which cannot be represented with classical type-1 fuzzy set. Hence, type-2 fuzzy set is proposed to define this type of complex uncertainty. Based on the complex uncertainty of data, fuzzy set theory type-2 with fuzzy number type-2 concept is used to represent the data with complex uncertainty. This process re-defines the data as type-2 fuzzy data which is also the result obtained by generalizing type-1 fuzzy data. Therefore, B-spline function is chosen to show the development of type-2 B-spline curve model via generalization. It is then followed by a number of processes, i.e. fuzzification, reduction and defuzzification are defined to model type-2 fuzzy B-spline curve to obtain a crisp type-2 fuzzy curve.