In this paper, first, we propose an iterative method based on quadrature formula for solving two-dimensional linear fuzzy Fredholm integral equations (2DLFFIE). Then, we prove the error estimation of the method. In addition, we show the numerical stability analysis of the method with respect to the choice of the first iteration. Finally, supporting examples are also provided. Keywords Fuzzy-number-valued functions Á Numerical method Á Two-dimensional linear fuzzy Fredholm integral equations Á Quadrature iterative method 1. u is normal, i.e. 9x 0 2 R; uðx 0 Þ ¼ 1. 2. uðgx þ ð1 À gÞyÞ ! minfuðxÞ; uðyÞg8x; y 2 R; 8g 2 ½0; 1 (u is called a convex fuzzy subset). 3. u is upper semicontinuous on R, i.e., 8x 0 2 R and 8 [ 0, 9 neighborhood Vðx 0 Þ : uðxÞ uðx 0 Þ þ ; 8x 2 Vðx 0 Þ.

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In this study, at first, we propose a new approach based on the two-dimensional fuzzy Lagrange interpolation and iterative method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equation (2DLFFIE). Then, we prove convergence analysis and numerical stability analysis for the proposed numerical algorithm by two theorems. Finally, by some examples, we show the efficiency of the proposed method.

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