Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30172
The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation

Authors: N. Parandin, M. A. Fariborzi Araghi

Abstract:

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080235

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1054

References:


[1] S. Abbasbandy, E. Babolian, and M. Alavi, "Numerical method for solving linear Fredholm fuzzy integral equations of the second kind," Chaos, Solitons and Fractals, Vol. 31, pp. 138-146, 2007.
[2] S. Abbasbandy, B. Asady, "A not on "A new approach for difuzzification," Fuzzy Sets and System, Vol. 128, pp.131-132, 2002.
[3] D. Dubois and H. Prade, "Towards fuzzy differential calculus}, Fuzzy Sets and System, Vol. 8, pp.1-7. 1982.
[4] M. Friedman, M. Ming and A. Kandel, "Fuzzy linear systems"Fuzzy Sets and Systems, Vol. 96, pp. 201-209, 1998.
[5] M. Friedman, M. Ming and A. Kandel, "Numerical solutions of fuzzy differential and integral equations", Fuzzy Sets and System Vol. 106, pp. 35-48, 1999.
[6] R. Goetschel, W. Voxman, "Elementary calculus" Fuzzy Sets and System, Vol. 18, pp. 31-43, 1986
[7] O. Kaleva, "Fuzzy differential equations", Fuzzy Sets and System, Vol. 24, pp. 301-317, 1987
[8] G. J. Klir, U. S. Clair, B. Yuan, "Fuzzy set theory: foundations and Applications," Prentice-Hall Inc. 1997.
[9] M. Ma, M. Friedman and A. Kandel, "A new fuzzy arithmetic", Fuzzy Sets and System, Vol. 108(1999), pp. 83-90.
[10] M.Ma, A.Kandel and M.Fiedman, "Correction to "A new approach for defuzzification", Fuzzy Sets and System, Vol. 128, pp.133-134. 2002
[11] M.Ma, A. Kandel and M. Fiedman, "A new approach for defuzzification," Fuzzy Sets and System Vol. 111, pp. 351-356. 2000.
[12] M. Matloka, "On fuzzy integrals", In: proc. 2nd polish Symp. On interval and fuzzy Mathematics, Politechnika Poznansk, pp. 167- 170. 1987.
[13] S. Nanda, "On integration of fuzzy mappings," Fuzzy Sets and System, Vol. 32. pp. 95-101. 1999.
[14] M. T. Rashed, "Numerical solutions of functional integral equations", Applied Mathematics and Computation, Vol. 156, pp.507-512. 2004.
[15] H. Sadeghi Goghary and M. Sadeghi Goghary, "Two computational methods for solving linear Fredholm fuzzy integral equations of the second kind," Applied Mathematics and Computation, Vol. 182, pp.791-796. 2006.
[16] W. Congxin and M. Ma, "On embedding problem of fuzzy number spaces", Fuzzy Sets and Systems, Vol. 44, pp. 33-38, 1991; Vol. 45, pp. 189-202, 1992