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

 

Received: 15 May 2009 /Accepted: 29 December 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

 

REFERENCES

 

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 Matematikke XV. 4-7 Jun, 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.

 

*Corresponding author; email: fatah@umt.edu.my

 

 

 

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