Sains Malaysiana 39(4)(2010): 661–670
Penyelesaian Masalah Data
Ketakpastian Menggunakan Splin-B Kabur
(Solving Problems of Uncertain
Data using Fuzzy B-Spline)
Abd. Fatah Wahab*
Jabatan Matematik, Fakulti Sains dan Teknologi
Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Malaysia
Jamaludin Md. Ali & Ahmad Abd. Majid
Sekolah Sains Matematik, Universiti Sains Malaysia, 11800 USM
Pulau Pinang, Malaysia
Abu Osman Md. Tap
Jabatan IT, Universiti Islam Antarabangsa Malaysia, 53100
Gombak, Selangor, Malaysia
Diserahkan: 15 Mei 2009 / Diterima: 29 Disember 2009
ABSTRAK
Pembinaan model geometri berbantukan komputer (CAGD) dengan
titik data yang mempunyai ketakpastian adalah sukar dan mencabar. Dalam kertas
ini, pembinaan model splin-B kabur sebagai perwakilan matematik bagi lengkung
dengan data ketakpastian menggunakan titik kawalan kabur dan titik kawalan
penyahkaburan dibincangkan. Lengkung splin-B kabur atau splin-B penyahkaburan
kubik untuk masalah data ketakpastian akan diperihalkan dengan menggunakan
kaedah penghampiran splin-B kubik yang ditakrif menerusi titik kawalan kabur
dan titik kawalan penyahkaburan. Bagi menyelesaikan masalah mengenai titik data
ketakpastian pula, kaedah pengkaburan dan penyahkaburan titik data berkomponen
kabur (penyahkaburan) beserta modelnya diperkenalkan. Bagi menguji tahap
keberkesanan model, beberapa contoh lengkung simulasi data tersebut juga
dibincangkan.
Kata kunci: Data ketakpastian; penyahkaburan; splin-B kabur; titik kawalan kabur
ABSTRACT
The
construction of a geometric model in Computer Aided Geometrical Design (CAGD)
with uncertain data points are difficult and challenging. In this paper, the
construction of a fuzzy B-spline model as a mathematical representation for the
curve of uncertain data using fuzzy control points and deffuzified control
points is discussed. Cubic fuzzy B-spline or defuzzified B-spline curve for
uncertainty data problems will be described using the cubic fuzzy B-spline
approximation methods which are defined through fuzzy and defuzzification
control points. For solving uncertain data, a method of fuzzification and
defuzzification of component fuzzy (defuzzify) data point together with their
model was introduced. For testing the effectiveness of the model, several
examples of curve simulation of the given data are also discussed.
Keywords:
Defuzzification; fuzzy B-Splie; fuzzy control points; uncertain data
RUJUKAN
Abd. Fatah Wahab, Ali, J.M., Majid, A.A. & Tap, A.O.M. 2004.
Fuzzy set in geometric modelling. International
Conference on Computer Graphics, Imaging and Visualization. CGIV 2004,
26-29 July, Penang Malaysia. IEEE Computer Society.
Abd. Fatah Wahab, Ali, J.M., Tap, A.O.M. & Majid, A.A. 2005.
Geometric modeling of uncertain region. LUMS
International of Mathematical Modeling and IT. 5-7 November, Lahore
University of Management Sciences (LUMS).
Abd. Fatah Wahab, Ali, J.M., Tap, A.O.M. & Majid,
A.A. 2007. Penyesuaian data ketakpastian melalui splin kabur. Prosiding. Simposium Kebangsaan Sains
Matematik ke XV. 4-7 Jun 2007, UiTM, PPMM & PERSAMA.
Anile, A.M., Falcidieno, B., Gallo, G., Spagnuolo, M. &
Spinello, S. 2000. Modelling uncertain data with fuzzy B-splines, Fuzzy Sets System 113: 397-410.
Anile, A.M., Deodato, S. & Privitera, G. 1995. Implementing
fuzzy arithmetic Fuzzy Sets System 72:
239-250.
Castro, J.L. 1995 Fuzzy logic controlers are universal
approximators. IEEE Trans. System Man.
and Cybernetics 25(4): 629-635.
Gallo, G. & Spinello, S. 2000. Fuzzy B-spline: A surface
model encapsulating uncertainty. Graphical
Models 62: 40-55.
Jaccas, J., Monreal, A. & Recasens, J. 1997. A model for
CAGD using fuzzy logic. International
Journal of Approximate Reasoning 16: 289-308.
Jaccas, J. & Recasens, J. 1993. Fuzzy numbers and equality
relations. Proceedings FUZZ’IEEE-93 Congress. San Francisco, CA.
Jamaludin & Abd. Fatah Wahab. 2005. Kecekapan
matematik dalam reka bentuk untuk keperluan industri. Prosiding Seminar Matematik dan Masyarakat, 26-27 Februari anjuran
Jabatan Matematik, FST, KUSTEM di Gem Beach Resort Kuala Terengganu, Malaysia.
Zadeh, L.A. 1965. Fuzzy Sets. Information and Control 8(3): 338-353.
*Pengarang untuk surat-menyurat; email: fatah@umt.edu.my
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