We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2), and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.

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Due to the recent financial crisis and regulatory concerns of Basel II, credit risk assessment has become one of the most important topics in the financial risk management. Quantitative credit scoring models are widely used to assess credit risk in financial institutions. In this paper we introduce Time Adaptive self organizing Map Neural Network to cluster creditworthy customers against non credit worthy ones. We test this Neural Network on Australian credit data set and compare the results with other clustering Algorithm's include K-means, PAM, SOM against different internal and external measures. TASOM has the best performance in clusters customers.

Please cite this article as: S.M. Sadatrasoul, R. Ezzati, Numerical solution of two-dimensional nonlinear Hammerstein fuzzy integral equations based on optimal fuzzy quadrature formula, Journal of Computational and Applied Mathematics (2015), http://dx. AbstractIn this paper, our aim is to provide an efficient iterative method of successive approximations to approximate solution of linear and nonlinear two-dimensional Hammerstein fuzzy integral equations by defining and developing an optimal quadrature formula for classes of two-dimensional fuzzy-number-valued functions of Lipschitz type. After the introduction of the optimal formula, we prove the convergence of the method of successive approximations used to approximate the solution of two-dimensional Hammerstein fuzzy integral equations and investigate the numerical stability of the presented method with respect to the choice of the first iteration. Finally, some illustrative numerical experiments confirm the theoretical results and demonstrate the accuracy of the method.Keywords: Two dimensional Hammerstein fuzzy integral equations (2DHFIE); Optimal quadrature formula; Banach fixed point theorem; The method of successive approximations; Iterative method.

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