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

Rozaimi Zakaria,Isfarita Ismail,Abd Fatah Wahab,Mohammad Izat Emir Zulkifly

doi:10.3390/math9091054

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.

Highlights

Mathematics 2021, 9, 1054. https://Data points are the representation of the visible object in a digital system
This type-2 fuzzy model meets the processes of fuzzification, type-reduction and defuzzification to obtain the crisp type-2 fuzzy curve and surface solution
This paper proposed a new method for defining complex uncertainty data, and modeled it on the hybrid model constructed called type-2 fuzzy interpolation B-spline surface (T2FIBsS)

Summary

Introduction

Data points are the representation of the visible object in a digital system. The data points representing an object are not necessarily precise due to their characteristics, which are uncertain, leading to complexity. The complexities that are found in the data are due to various possible reasons, e.g., inappropriate analysis, human perception and logical assumption [1,2], limitations of tool accuracy, and the nature of data collection itself [3,4] with different types of uncertainty being based on BIPM The specific meaning of ‘complex’ in complex uncertainty data is the stack of the uncertainty of two arguments of the collected data points. It is impossible to accurately model the complex uncertainty data using an appropriate standard curve or surface function, such as the B-spline function, unless we formulate a new definition of the B-spline function with the complex uncertainty meaning

Methods

Results

Conclusion