Surface modeling is an effective method that is frequently employed in industry. In this paper, approximation of picture fuzzy Bézier surface is shown where the control net of picture fuzzy relation is determined by concept of picture fuzzy set. Afterwards, the control net and the Bézier function are blended to generate picture fuzzy Bézier surface. At the end of this studies, picture fuzzy Bézier surface consist the positive, neutral, negative, and refusal membership surface is visualized. Some numerical example of picture fuzzy Bézier surface approximation and their respective properties are also shown.
REFERENCES
1.
D.
Salomon
, Curves and Surfaces for Computer Graphics
((Springer Science+Business Media, Inc
., New York
, 2006
), pp. 11
–15
.2.
Q.
Chen
and G.
Wang
, A class of Bézier-like curves
(Comput. Aided Geom. Des
. 2003
) 20, 29
–39
.3.
R. T.
Wang
, “Title of Chapter,” in Classic Physiques
, edited by R. B.
Hamil
(Publisher Name
, Publisher City
, 1999
), pp. 212
–213
.X.
Han
, Y.
Ma
, X.
Huang
, A novel generalization of Bézier curve and surface (J. Comput. Appl. Math
. 2008
) 217
, 180
–193
.4.
J.
Zhang
, C-curves: An extension of cubic curves
. Comput. Aided Geom. Des.
1996
, 13
, 199
–217
5.
Farin
, G.
, Hoschek
, J.
, Kim
, M.S.
(Eds.) Handbook of Computer aided Geometric Design
; Elsevier
: Amsterdam, The Netherlands
, 2002
6.
Ameer
, M.
, Abbas
, M.
, Miura
, K. T.
, Majeed
, A.
, Nazir
, T.
Curve and Surface Geometric Modeling via Generalized Bézier-like Model. Mathematics
2022
, 10
, 1045
.7.
Maqsood
S.
, Abbas.
M.
, Hu.
G.
, Ramli.
A. L. A.
, A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications
. Hindawi Mathematical Problems in Engineering.
Volume 2020
, article ID 4036434, 25
pages.8.
Zadeh
, L. A.
Fuzzy Sets
. Information Control
, 8
: 338
–356
. 1965
. 19659.
Li
, D. F.
Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment
. Fuzzy Optimization and Decision Making
, 7
: 17
–34
. 2008
.10.
Rosli
, S. N. I.
, and Zulkifly
, M. I. E.
Neutrosophic Bicubic B´ezier Surface Approximation Model for uncertainty data
. Matematika, MJIM
, volume 39
, Number 3
, 281
–291
.11.
Rosli
, S. N. I.
, and Zulkifly
, M. I. E.
3-Dimensional Quartic B´ezier Curve Approximation Model by Using Neutrosophic Approach
. Neutrosophic Systems with Applications.
2023
. 11
: 11
–21
.12.
Rosli
, S. N. I.
, and Zulkifly
, M. I. E.
Interval Neutrosophic Cubic Bézier Curve Approximation Model for Complex Data
, Malaysian Jurnal of Fundamental and Applied Sciences
, vol. 20
(2024
), 336
–346
.13.
Coung
, B. C.
and Kreinovich
, V.
Picture Fuzzy Sets-A new concept for Computational Intelligence Problems
. Department Technical Reports(CS)
, 809
. 2013
14.
Coung
, B. C.
and Kreinovich
, V.
Picture Fuzzy Set. Picture Fuzzy Sets
. Journal of Computer Science and Cybernetics.
2014
15.
16.
W.
Atanassov
, K. More on Intuitionistic Fuzzy Sets
. Fuzzy Sets and Systems
, 33
: 37
–46
. 1989
17.
W
Atanassov
, K. T.
and Georgiev
, C.
Intuitionistic Fuzzy Proloq
. Fuzzy Sets and Systems
, 53
:121
–128
. 1993
18.
Wahab
, A. F.
and Zulkifly
, M. I. E.
Cubic Bézier Curve Interpolation by Using Intuitionistic Fuzzy Control Point Relation
. AIP Proceedings
, 1974
, 020031
(2018
), 19.
Wahab
, A. F.
and Zulkifly
, M. I. E.
Intuitionistic fuzzy b-spline curve approximation model for complex uncertainty data problems
. Far East Journal of Mathematical Sciences (FJMS)
, 106
(1
):217
–235
. 2018b
20.
L.
Piegl
and W.
Tiller
. The NURBS Book
(Springer-Verlag Berlin Heidelberg
, Germany
, 1995
).
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