Normal type-2 Fuzzy Rational B-Spline Curve

TL;DR

This paper introduces normal type-2 fuzzy data points and applies fuzzification, type-reduction, and defuzzification processes to model rational B-spline curves, providing a new approach for fuzzy data representation.

Contribution

It proposes a novel form of type-2 fuzzy data points (NT2FDPs) and integrates them into rational B-spline curve modeling with new fuzzification and defuzzification methods.

Findings

Successful representation of NT2FDPs using rational B-spline curves

New fuzzification and defuzzification methods for type-2 fuzzy data points

Enhanced modeling of fuzzy data with improved accuracy

Abstract

In this paper, we proposed a new form of type-2 fuzzy data points(T2FDPs) that is normal type-2 data points(NT2FDPs). These brand-new forms of data were defined by using the definition of normal type-2 triangular fuzzy number(NT2TFN). Then, we applied fuzzification(alpha-cut) and type-reduction processes towards NT2FDPs after they had been redefined based on the situation of NT2FDPs. Furthermore, we redefine the defuzzification definition along with the new definitions of fuzzification process and type-reduction method to obtain crisp type-2 fuzzy solution data points. For all these processes from the defining the NT2FDPs to defuzzification of NT2FDPs, we demonstrate through curve representation by using the rational B-spline curve function as the example form modeling these NT2FDPs.