In this paper, the cubic Bézier curve interpolation method for intuitionistic fuzzy data is introduced based on the theory of intuitionistic fuzzy sets. The intuitionistic fuzzy point relation and intuitionistic fuzzy control point relation is defined based on intuitionistic fuzzy point, intuitionistic fuzzy number and intuitionistic fuzzy relation concepts. Next, the intuitionistic fuzzy control point relation is blended with the Bernstein basis function and the intuitionistic fuzzy cubic Bézier curve is produced. Then, the intuitionistic fuzzy data is interpolated and visualized by using the intuitionistic fuzzy cubic Bézier curve.
REFERENCES
1.
L. A.
Zadeh
, Information and Control
, 8
, 338
–353
(1965
).2.
K. T.
Atanassov
, “Intuitionistic Fuzzy Sets”, VII ITKR’s Session
, Sofia, Bulgarian
, 1983
.3.
A. M.
Anile
, B.
Falcidieno
, G.
Gallo
, M.
Spagnuolo
, S.
Spinello
, 113
, 397
–410
(2000
).4.
O.
Kaleva
, Fuzzy Sets and Systems
, 61
, 63
–70
(1994
).5.
A. F.
Wahab
, R.
Zakaria
and J. M.
Ali
, “Fuzzy Interpolation Rational Bezier Curve
” in Imaging and Visualization, 7ᵗʰ International Conference on Computer Graphics
, Sydney, NSW
, 2010
, pp. 63
–67
.6.
7.
R.
Zakaria
and A.F.
Wahab
, Applied Mathematical Sciences
, 7
, 2229
–2238
(2013
).8.
S.
Abbas
, M. Z.
Hussain
and M.
Irshad
, Image Interpolation by Rational Ball Cubic B-spline Representation and Genetic Algorithm
, Alexandria Engineering Journal
, 2017
.9.
A. M.
Bica
and C.
Popescu
, Fuzzy Sets and Systems
, 310
, 60
–73
(2017
).10.
11.
M.
Gaeta
, V.
Loia
and S.
Tomasiello
, Information Sciences
, 339
, 19
–30
2016
.12.
A. F.
Wahab
, M. I. E.
Zulkifly
and M. S.
Husain
, “Bezier Curve Modeling for Intuitionistic Fuzzy Data Problem
,” in AIP Conference Proceedings 1750
, (American Institute of Physics
, 2016
) pp. 030047-1
–030047-2
.13.
M. I. E.
Zulkifly
and A. F.
Wahab
, Malaysian Journal of Fundamental and Applied Sciences (MJFAS)
, 11
, 21
–23
(2015
).14.
A. F.
Wahab
and M.I. E.
Zulkifly
, Applied Mathematical Sciences
, 11
, 39
–57
(2017
).15.
K. T
Atanassov
, Fuzzy Sets and Systems
, 20
, 87
–96
(1986
).16.
K. T.
Atanassov
, “Intuitionistic Fuzzy Sets: Theory and Applications”, Physica-Verlag HD
, 1999
, pp. 1
–9
.17.
K. T.
Atanassov
, “On Intuitionistic Fuzzy Sets Theory”, Springer
, 2012
, pp. 1
–12
.18.
D.
Dubois
and H.
Prade
, International Journal of Systems Science
, 9
, 613
–626
(1978
).19.
D.
Dubois
and H.
Prade
, Fuzzy Sets and Systems
, 24
, 279
–300
(1987
).20.
A. K.
Shaw
and T. K.
Roy
, International Journal of Fuzzy Mathematics and Systems
, 2
, 363
–382
(2012
)21.
L. A.
Zadeh
, Information Sciences
, 3
, 177
–200
(1971
).22.
A.
Rosenfeld
, “Fuzzy Graphs”, in Fuzzy Sets and their Applications to Cognitive and Decision Processes
, Academic Press
, pp 77
–95
. 1975
.23.
A.
Kauffman
, Introduction to the Theory of Fuzzy Subsets
, Vol I
. New York, San Francisco, London
. 1975
.24.
H. J.
Zimmermann
, “Fuzzy Set Theory and Its Application”, Kluwer Academic
, New York, NY, USA
, 1985
, pp. 47
–56
.25.
P.
Burillo
and H.
Bustince
, Orderings in the Referential Set Induced by an Intuitionstic Fuzzy Relation
Notes, on IFS
, 1
(2
), 93
–103
(1995
).26.
D.
Çoker
and M.
Demirci
, On intuitionistic Fuzzy Points
, Notes on IFS
, 1
(2
), 79
–84
(1995
).27.
D.
Çoker
, A Note on Intuitionistic Sets and Intuitionistic Points
, Tr. J. of Mathematics
, 20
, 343
–351
(1996
).28.
S.
Bayhan
and D.
Çoker
, On Fuzzy Separation Axioms in Intuitionistic Fuzzy Topological Spaces
, Busefal
, 67
, 77
–87
(1996
).29.
S.
Das
, “Intuitionistic Fuzzy Topological Spaces
”, Master thesis, National Institute of Technology
, Rourkela
, 2013
.30.
P. P.
Ming
and L. Y.
Ming
, Fuzzy Topology. I. Neighborhood Structure of a Fuzzy Point and Moore-Smith Convergence
, Journal of Mathematical Analysis and Applications
, 76
(2
), 571
–599
(1980
).31.
A. F.
Wahab
, J. M.
Ali
and A. A.
Majid
, “Fuzzy Geometric Modeling
” in Imaging and Visualization, International Conference on Computer Graphics
, 2004
, pp. 227
–232
.32.
A. F.
Wahab
, J. M.
Ali
, A. A.
Majid
and A. O. M.
Tap
, “Fuzzy Set in Geomeric Modeling
” in Imaging and Visualization, 6ᵗʰ International Conference on Computer Graphics
, Tianjin
, 2009
, pp. 276
–280
.33.
A. F.
Wahab
, J. M.
Ali
, A. A.
Majid
and A. O. M.
Tap
, Penyelesaian Masalah Data Ketakpastian Menggunakan Splin-B Kabur
, Sains Malaysiana
, 39
(4
), 661
–670
(2010
).
This content is only available via PDF.
© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.