Finite Difference Method For Solving Fuzzy
Linear Boundary Value Problems

Rasha H.Ibraheem

doi:https://doi.org/10.14445/22315373/IJMTT-V65I5P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 5 | Year 2019 | Article Id. IJMTT-V65I5P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I5P508

Finite Difference Method For Solving Fuzzy Linear Boundary Value Problems

Rasha H.Ibraheem

Citation :

Rasha H.Ibraheem, "Finite Difference Method For Solving Fuzzy Linear Boundary Value Problems," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 5, pp. 65-71, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I5P508

Abstract

In this paper, the Finite Difference method is considered to solve the nonhomogeneous for Second order fuzzy boundary value problems, In which the fuzziness appeared together in the boundary conditions and in the nonhomogeneous term of the differential equation. The method of solution depends on transforming the fuzzy problem to equivalent crisp problems using the concept of α-level sets.

Keywords

the Finite Difference Method; Fuzzy sets; α-level sets; second order fuzzy boundary value problems.

References

[1] Pal S. K. and Majumder D.K Fuzzy Mathematical Approach to Pattern Recognition , John Wi ley and sons, Inc., New York, 1986.
[2] Dubois, D. and Prade, H., Fuzzy Sets and Systems; Theory and Applications , Academic Press, Inc., 1988.
[3] Pearson, D. W.: “A Property of Linear Fuzzy Differential Equations”, Appl. Math. Lett., Vol.10, No.3, 1997 , pp.99-103.
[4] Zimmerman, H. J., "Fuzzy Set Theory and Its Applications", Kluwer-Nijhcff Publishing, USA, 1988.
[5] Kandel A., Fuzzy Mathematical Techniques with Applications , Addison Wesley Publishing Company, Inc., 1986.
[6] Zadeh, L. A., "Fuzzy Sets", Information Control, 8 (1965), 338-353.
[7] Yan, J., Ryan, M. and Power, J., Using Fuzzy Logic: Towards Intelligent Systems , Prentice Hall, Inc., 1994.
[8] Al-Adhami R. H., "Numerical Solution of Fuzzy Boundary Value Problems", M.Sc. Thesis, College of Science, Al-Nahrain University, 2007.
[9] William,E.B.and Richard,C.D.,"Elementary Differential Equation and Boundary Value problems",Jone wiley and Sons,Inc,1961.