Application of Gaussian Quadratures in Solving Fuzzy Fredholm Integral Equations

In this paper first of all the integral term in the fuzzy Fredholm integral equation (FFIE) is approximated by one of the Gaussian methods. FFIE is transformed to a dual fuzzy linear system that it can be approximated by the method that proposed in [7]. In the special case, Chebyshev-Gauss quadrature is applied to approximate the mentioned integral.

[1]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[2]  Tofigh Allahviranloo,et al.  The Adomian decomposition method for fuzzy system of linear equations , 2005, Appl. Math. Comput..

[3]  P. V. Subrahmanyam,et al.  On some fuzzy functional equations , 1994 .

[4]  Tofigh Allahviranloo,et al.  Successive over relaxation iterative method for fuzzy system of linear equations , 2005, Appl. Math. Comput..

[5]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[6]  Xizhao Wang,et al.  Iteration algorithms for solving a system of fuzzy linear equations , 2001, Fuzzy Sets Syst..

[7]  Abraham Kandel,et al.  Fuzzy linear systems , 1998, Fuzzy Sets Syst..

[8]  Jong Yeoul Park,et al.  The approximate solutions of fuzzy functional integral equations , 2000, Fuzzy Sets Syst..

[9]  Abraham Kandel,et al.  Duality in fuzzy linear systems , 2000, Fuzzy Sets Syst..

[10]  Esmail Babolian,et al.  Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method , 2005, Appl. Math. Comput..

[11]  Young Chel Kwun,et al.  Existence of solutions of fuzzy integral equations in Banach spaces , 1995 .

[12]  Jong Yeoul Park,et al.  On the existence and uniqueness of solutions of fuzzy Volterra-Fredholm integral equations , 2000, Fuzzy Sets Syst..

[13]  Saeid Abbasbandy,et al.  LU decomposition method for solving fuzzy system of linear equations , 2006, Appl. Math. Comput..

[14]  Ke Wang,et al.  Symmetric successive overrelaxation methods for fuzzy linear systems , 2006, Appl. Math. Comput..

[15]  Tofigh Allahviranloo,et al.  A comment on fuzzy linear systems , 2003, Fuzzy Sets Syst..

[16]  Jong Yeoul Park,et al.  A note on fuzzy integral equations , 1999, Fuzzy Sets Syst..

[17]  Tofigh Allahviranloo,et al.  Block Jacobi two-stage method with Gauss-Sidel inner iterations for fuzzy system of linear equations , 2006, Appl. Math. Comput..