In general, the application of fuzzy sets in geometric modeling contributes to many areas such as data analysis and prediction. Hence, this study proposed an application of type-2 intuitionistic fuzzy set (T2IFS) in geometric modeling onto complex uncertainty data in which the data are defined using the type-2 fuzzy concept or in other words, there is uncertainty in uncertainty data. T2IFSs are the generalized forms of fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets, and interval-valued intuitionistic fuzzy sets. Based on the notion of T2IFS, type-2 intuitionistic fuzzy point (T2IFP) is defined to produce a type-2 intuitionistic fuzzy control point (T2IFCP). Then, the T2IFCP will be blended with the Bernstein blending function, resulting in a type-2 intuitionistic interpolation fuzzy Bézier curve, through the interpolation method. Numerical examples and algorithms to generate the curve will be further shown in this paper.

Topics
Functions and functionals, Interpolation, Fuzzy control
1.
Tas
F.
,
Topal S.
Bézier
Curve Modeling for Neutrosophic Data Problem
.
NSS.
2017
;
16
:
3
–
5
.
Google Scholar
 
2.
Szmidt
E.
Uncertainty and Information: Foundations of Generalized Information Theory
(
Klir
,
G.J.
;
2006
).
IEEE Transactions on Neural Networks.
2007;
18
(
5
):
1551
–
1551
.
Google Scholar
Crossref
Search ADS
 
3.
Zadeh
L.A.
Fuzzy sets. Information and Control.
1965
;
8
(
3
):
338
–
353
.
Google Scholar
Crossref
Search ADS
 
4.
Zadeh
L.A.
Fuzzy logic and approximate reasoning. Synthese.
1975
;
30
(
3
):
407
–
428
.
Google Scholar
 
5.
Mendel
J.
Type 2 Fuzzy Sets and Systems: An Overview [corrected reprint]
.
IEEE Computational Intelligence Magazine.
2007
;
2
(
2
):
20
–
29
.
Google Scholar
 
6.
Atanassov
K.T.
Intuitionistic fuzzy sets
.
Fuzzy Sets and Systems.
1986
;
20
(
1
):
87
–
96
.
Google Scholar
Crossref
Search ADS
 
7.
Cuong
B.C.
,
Anh
T.H.
,
Hai
B.D.
Some operations on type-2 intuitionistic fuzzy sets
.
Journal of Computer Science and Cybernetics.
2012
;
28
(
3
):
274
–
283
.
Google Scholar
Crossref
Search ADS
 
8.
Bakali
A.
,
Broumi
S.
,
Nagarajan
D.
,
Talea
M.
,
Lathamaheswari
M.
,
Kavikumar
J.
Graphical Representation of Type-2 Neutrosophic sets
.
NSS.
2021
;
42
:
28
–
38
.
Google Scholar
 
9.
Zakaria
R.
,
Wahab
A.F.
,
Gobithaasan
R.U.
Normal type-2 Fuzzy Rational B-Spline Curve.
2013
.
Google Scholar
 
10.
Zakaria
R.
,
Wahab
A.F.
,
Gobithaasan
R.U.
Normal type-2 fuzzy interpolating B-spline curve
.
AIP Conference Proceedings.
2015
;
1605
(
1
):
476
.
Google Scholar
 
11.
Zakaria
R.
,
Wahab
A.F.
,
Gobithaasan
R.U.
The Series of Fuzzified Fuzzy Bézier Curve
.
Jurnal Teknologi.
2015
;
78
(
2-2
).
Google Scholar
 
12.
Zakaria
R.
,
Wahab
A.F.
,
Gobithaasan
R.U.
Fuzzy B-spline surface modeling
.
Journal of Applied Mathematics.
2014
.
Google Scholar
 
13.
Zakaria
R.
,
Wahab
A.F.
,
Ismail
I.
,
Zulkifly
M.I.E.
Complex Uncertainty of Surface Data Modeling via the Type-2 Fuzzy B-Spline Model
.
Mathematics.
2021
;
9
(
9
):
1054
.
Google Scholar
Crossref
Search ADS
 
14.
Wahab
A.F.
,
Ali
J.M.
,
Majid
A.A.
Fuzzy geometric modeling
.
In: Proceedings of the 2009 6th International Conference on Computer Graphics, Imaging and Visualization: New Advances and Trends, CGIV2009.
2009
. p.
276
–
280
.
Google Scholar
 
15.
Wahab
A.F.
,
Zulkifly
M.I.E.
Intuitionistic fuzzy in spline curve/surface
.
Malaysian Journal of Fundamental and Applied Sciences.
2015
;
11
(
1
).
Google Scholar
 
16.
Wahab
A.F.
,
Zulkifly
M.I.E.
A new fuzzy Bézier curve modeling by using fuzzy control point relation
.
Applied Mathematical Sciences.
2017
;
11
:
39
–
57
.
Google Scholar
Crossref
Search ADS
 
17.
Wahab
A.F.
,
Zulkifly
M.I.E.
,
Ismail
N.B.
Fuzzy Bézier curve interpolation modeling by using fuzzy control point relation
.
Advances and Applications in Discrete Mathematics.
2019
;
21
(
1
):
1
–
23
.
Google Scholar
Crossref
Search ADS
 
18.
Tolga
A.C.
Real options valuation of an IoT based healthcare device with interval Type-2 fuzzy numbers
.
Socio-Economic Planning Sciences.
2020
;
69
.
Google Scholar
 
19.
Singh
S.
,
Garg
H.
Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process
.
Applied Intelligence.
2016
;
46
(
4
):
788
–
799
.
Google Scholar
Crossref
Search ADS
 
20.
Roy
S.K.
,
Bhaumik
A.
Intelligent Water Management: a Triangular Type-2 Intuitionistic Fuzzy Matrix Games Approach
.
Water Resources Management.
2017
;
32
(
3
):
949
–
968
.
Google Scholar
Crossref
Search ADS
 
21.
Chaira
T.
Fuzzy set and its extension: The intuitionistic fuzzy set
.
Hoboken, NJ
:
Wiley-Blackwell
;
2019
.
Google Scholar
Crossref
Search ADS
 
22.
Wahab
A.F.
,
Zulkifly
M.I.E.
,
Husain
M.S.
Bézier curve modeling for intuitionistic fuzzy data problem
.
In: AIP conference proceedings.
2016
;
1750
.
Google Scholar
 
23.
Zakaria
R.
,
Wahab
A.F.
,
Gobithaasan
R.U.
Type-2 fuzzy Bézier curve modeling
.
AIP Conference Proceedings.
2013
;
1522
:
945
–
952
.
https://doi.org/10.1063/1.4801232
Google Scholar
Crossref
Search ADS
 
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