Friedman, Menahem; Ming, Ma; Kandel, Abraham Solutions to fuzzy integral equations with arbitrary kernels. (English) Zbl 0949.65137 Int. J. Approx. Reasoning 20, No. 3, 249-262 (1999). The authors propose a numerical integration scheme for solving fuzzy integral equations of Fredholm and Volterra type with arbitrary continuous kernels. It is shown that the scheme, based on the trapezoidal rule converges uniformly to the respective exact unique solution. Adequate numerical examples are given. Reviewer: Emil Minchev (Sofia) Cited in 38 Documents MSC: 65R20 Numerical methods for integral equations 28E10 Fuzzy measure theory 26E50 Fuzzy real analysis 45B05 Fredholm integral equations 45D05 Volterra integral equations Keywords:convergence; fuzzy integral equations of Fredholm and Volterra type; trapezoidal rule; numerical examples PDFBibTeX XMLCite \textit{M. Friedman} et al., Int. J. Approx. Reasoning 20, No. 3, 249--262 (1999; Zbl 0949.65137) Full Text: DOI References: [1] Dieudonué, J., Eléments Dánalyse, ((1960), Academic Press: Academic Press Vienna), 136 [2] Dubois, D.; Prade, H., Towards fuzzy differential calculus, Fuzzy Sets and Systems, 8, 225-233 (1982) · Zbl 0537.93003 [3] Friedman, M.; Kandel, A., Fundamentals of Computer Numerical Analysis, ((1994), CRC Press), 249-276 [4] Goetschel, R.; Voxman, W., Elementary calculus, Fuzzy Sets and Systems, 18, 31-43 (1986) · Zbl 0626.26014 [5] Hochstadt, H., Integral Equations, ((1973), Wiley: Wiley Boca Raton), 1-24 [6] Kaleva, O., Fuzzy differential equations, Fuzzy sets and Systems, 24, 301-317 (1987) · Zbl 0646.34019 [7] O. Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems 35 (199) 389-396.; O. Kaleva, The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems 35 (199) 389-396. · Zbl 0696.34005 [8] Kandel, A.; Byatt, W. J., Fuzzy differential equation, (Proceedings of the International Conference Cybernetics and Society. Proceedings of the International Conference Cybernetics and Society, Tokyo (November 1978)), 1213-1216 [9] M. Ming, M. Friedman, A. Kandel, Numerical methods for fuzzy integral equations, IEEE, Trans. System Man and Cybernetics, submitted.; M. Ming, M. Friedman, A. Kandel, Numerical methods for fuzzy integral equations, IEEE, Trans. System Man and Cybernetics, submitted. · Zbl 0878.28014 [10] Matloka, M., On fuzzy integrals, (Proceedings of the second Polish Symposion on Interval and Fuzzy Mathematics. Proceedings of the second Polish Symposion on Interval and Fuzzy Mathematics, Politechnika Poznansk (1987)), 167-170 [11] Nanda, S., On integration of fuzzy mappings, Fuzzy Sets and Systems, 32, 95-101 (1989) · Zbl 0671.28009 [12] Puri, M. L.; Ralescu, D., Differential for fuzzy function, J. Math. Anal. Appl., 91, 552-558 (1983) · Zbl 0528.54009 [13] Puri, M. L.; Ralescu, D., Fuzzy random variables, J. Math. Anal. Appl., 114, 409-422 (1986) · Zbl 0592.60004 [14] Seikkala, S., On the fuzzy initial value problem, Fuzzy Sets and Systems, 24, 319-330 (1987) · Zbl 0643.34005 [15] Congxin, W.; Ming, M., On the integrals, series and integral equations of fuzzy set-valued fucntions, J. of Harbin Inst. of Technology, 21, 11-19 (1990) [16] Congxin, W.; Ming, M., On embedding problem of fuzzy number spaces, part 2, Fuzzy Sets and Systems, 45, 189-202 (1992) · Zbl 0771.46045 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.