In order to model uncertainty in data, the fuzzy intuitionistic alpha-cut modeling interpolation rational Bezier curve process will be examined in this paper. In defining the uncertainty data and then modeling it using a chosen curve function, the basic theories and definitions that will be used are fuzzy set theory, fuzzy intuitionistic, and curve functions under geometrical modeling. This study has three main processes, the first of which is the definition of the uncertainty data using the fuzzy number concept. The fuzzy intuitionistic definition will then be used to calculate the alpha value (also known as the alpha-cut) for both membership values and non-membership values. Following the definition of fuzzy intuitionistic into an alpha-cut value, the fuzzification process will be applied to the data set. Defuzzification will be used after the fuzzification process to produce single values data that are defined as crisp fuzzy data for modeling. Rational Bezier interpolation will be used for visualization of the modeling data for each process in order to make analyses and conclusions.

Topics
Fuzzy set theory
1.
A. F.
Wahab
,
J. Md.
Ali
,
A. Abd.
Majid
,
A. O. Md.
Tap
, “
Fuzzy Set in Geometry Modeling
”,
Proceedings of the International Conference on Computer Graphics, Imaging and Visualization
, pp.
227
–
232
,
2004
.
https://doi.org/10.1109/CGIV.2004.1323990
Google Scholar
 
2.
L. A.
Zadeh
, “
Fuzzy Sets
”,
Information and Control
, vol.
8
, pp.
338
–
353
,
1965
.
https://doi.org/10.1016/S0019-9958(65)90241-X
Google Scholar
Crossref
Search ADS
 
3.
R.
Zakaria
,
A. F.
Wahab
 and
I.
Ismail
, “
Fuzzy B-Spline Curved Surface Modeling
”,
ASM Science Journal
, Vol
2
, pp.
114
–
119
,
2019
.
Google Scholar
 
4.
A.
Talibe
,
R.
Zakaria
,
A.
Bade
 and
S.
Zenian
, “
Integrated Uncertainty Fuzzy Bezier Curve Modeling
”,
ASM Science Journal
, Vol
12
, pp.
162
–
166
,
2019
.
Google Scholar
 
5.
A. F.
Wahab
 and
R.
Zakaria
, “
Fuzzy Tuning B-Spline Curve
”,
Innovation and Analytics Conference and Exhibition
, pp.
1
–
6
,
2015
.
Google Scholar
 
6.
R.
Zakaria
 and
A. F.
Wahab
, “
Pemodelan Titik Data Kabur Teritlak
”,
Sains Malaysiana
,
43
(
5
), pp.
799
–
805
,
2014
.
Google Scholar
 
7.
A. Y.
Ceylan
,
T.
Turhan
,
G. O.
Tukel
, “
On the Geometry of Rational Bezier Curves
”,
Honan Mathematical J.
, No.
1
, pp.
88
–
99
,
2021
.
Google Scholar
 
8.
D.
Solomon
, “
Curves and Surfaces for Computer Graphics
”,
Springer Science+Business Media Incorporation, Northridge
, pp.
217
–
219
,
2006
.
Google Scholar
 
9.
A. F.
Wahab
,
R.
Zakaria
 and
J. Md.
Ali
, “
Fuzzy Interpolation Rational Bezier Curve
”,
Seventh International Conference on Computer Graphics, Imaging and Visualization
, pp.
63
–
67
,
2010
.
Google Scholar
 
10.
J. S.
Kouh
 and
S. W.
Chou
, “
Computer-aided Geometric Design and Panel Generation for Hull Forms Based on Rational Cubic Bezier Curves
”,
Computer Aided Geometric Design
,
10
(
6
), pp.
537
–
549
,
1993
.
https://doi.org/10.1016/0167-8396(93)90030-7
Google Scholar
Crossref
Search ADS
 
11.
G.-J.
Wang
 and
G.-Z
Wang
, “
The Rational Cubic Bezier Representation of Conics
”,
Computer Aided Geometric Design
,
9
(
6
), pp.
447
–
455
,
1992
.
https://doi.org/10.1016/0167-8396(92)90043-O
Google Scholar
Crossref
Search ADS
 
12.
M.I.E.
Zulkifly
,
A. F.
Wahab
,
R.
Zakaria
, “
B-Spline Curve Interpolation Model by using Intuitionistic Fuzzy Approach
”,
IAENG International Journal of Applied Mathematics
, vol.
50
, pp.
1
–
7
,
2020
.
Google Scholar
 
13.
K. T.
Atanassov
, “
Type-1 Fuzzy Sets and Intuitionistic Fuzzy Sets
”,
Algorithms
,
10
(
106
), pp.
1
–
12
,
2017
.
Google Scholar
Crossref
Search ADS
 
14.
T.
Chaira
, “
Fuzzy Sets and Its Extension
”,
The Intuitionistic Fuzzy Sets
, pp.
1
–
24
,
2019
.
Google Scholar
 
15.
E. W.
Weisstein
, “
Triangle Centroid
”, Retrieved from https://mathworld.wolfram.com/TriangleCentroid.html, Date accessed: 10 May 2022,
2022
.
16.
R.
Zakaria
,
N.A.
Suhaimi
,
A. N.
Jifrin
 and
S. N.
Jaman
, “
The Determining of Alpha Value for Alpha-cut Operation by Using Triangular Polygon Centroid
”,
Seminar of Science and Technology
, pp.
233
–
236
,
2021
.
Google Scholar
 
17.
M. I. E.
Zulkifly
,
A. F.
Wahab
 and
R.
Zakaria
, “
B-Spline Curve Interpolation Model by using Intuitionistic Fuzzy Approach
”,
IAENG International Journal of Applied Mathematics
,
50
(
4
), pp.
1
–
7
,
2020
.
Google Scholar
 
18.
R.
Elaiyaperumal
,
P.
Gajivaradhan
 and
M.
Suguna
, “
Defuzzification by Area of Region (AOR) in an Intuitionistic Fuzzy Environment
”,
The International Journal of Analytical and Experimental Modal Analysis
,
XI
(
IX
), pp.
3282
–
3288
,
2019
.
Google Scholar
 
19.
Z.
Sen
, “
Fuzzy Logic and Hydrological Modeling
”,
Taylor and Francis Group LLC
, pp.
206
,
2010
.
Google Scholar
 
20.
M.
Sarfraz
,
Z.
Habib
 and
M.
Hussain
, “
Piecewise Interpolation for Designing of Parametric Curves
”,
Information Visualization. Proceedings. 1998 IEEE Conference
, pp.
307
–
313
,
1998
.
Google Scholar
 
This content is only available via PDF.
©2024 Authors. Published by AIP Publishing.
2024
Author(s)
You do not currently have access to this content.