Bede, Barnabás; Gal, Sorin G. Quadrature rules for integrals of fuzzy-number-valued functions. (English) Zbl 1050.28009 Fuzzy Sets Syst. 145, No. 3, 359-380 (2004). Summary: We introduce some quadrature rules for the Henstock integral of fuzzy-number-valued mappings by giving error bounds for mappings of bounded variation and of Lipschitz type. We also consider generalizations of classical quadrature rules, such as midpoint-type, trapezoidal and three-point-type quadrature. Finally, we study \(\delta\)-fine quadrature rules and we present some numerical applications. Cited in 53 Documents MSC: 28E10 Fuzzy measure theory 26A39 Denjoy and Perron integrals, other special integrals 65D30 Numerical integration 65D32 Numerical quadrature and cubature formulas 26D15 Inequalities for sums, series and integrals 41A55 Approximate quadratures Keywords:Henstock integral; numerical integration; quadrature formula; fuzzy-number-valued functions; fuzzy integral equations PDFBibTeX XMLCite \textit{B. Bede} and \textit{S. G. Gal}, Fuzzy Sets Syst. 145, No. 3, 359--380 (2004; Zbl 1050.28009) Full Text: DOI References: [1] Anastassiou, G. A.; Gal, S. G., On a fuzzy trigonometric approximation theorem of Weierstrass-type, J. Fuzzy Math., 9, 3, 701-708 (2001) · Zbl 1004.42005 [2] P. Cerone, S.S. Dragomir, Three point quadrature rules involving, at most, a first derivative, RGMIA Research Report Collection, Vol. 2, No. 4, 1999 (http://rgmia.vu.edu.au; P. Cerone, S.S. Dragomir, Three point quadrature rules involving, at most, a first derivative, RGMIA Research Report Collection, Vol. 2, No. 4, 1999 (http://rgmia.vu.edu.au [3] Cerone, P.; Dragomir, S. S., Midpoint-type rules from an inequalities point of view, (Anastassiou, G. A., Handbook of Analytic-Computational Methods in Applied Mathematics (2000), Chapman & Hall, CRC Press: Chapman & Hall, CRC Press Boca Raton, London, New York, Washington DC), (Chapter 4) · Zbl 0966.26015 [4] Cerone, P.; Dragomir, S. S., Trapezoidal-type rules from an inequalities point of view, (Anastassiou, G. A., Handbook of Analytic-Computational Methods in Applied Mathematics (2000), Chapman & Hall, CRC Press: Chapman & Hall, CRC Press Boca Raton, London, New York, Washington DC), (Chapter 3) · Zbl 0966.26014 [5] Devore, R. A.; Lorentz, G. G., Constructive Approximation, Polynomials and Splines Approximation (1993), Springer: Springer Berlin, Heidelberg · Zbl 0797.41016 [6] D. Dubois, H. Prade, Fuzzy Numbers: an Overview, in Analysis of Fuzzy Information, Vol. 1, CRC Press, Boca Raton, FL, 1987, pp. 3-39.; D. Dubois, H. Prade, Fuzzy Numbers: an Overview, in Analysis of Fuzzy Information, Vol. 1, CRC Press, Boca Raton, FL, 1987, pp. 3-39. · Zbl 0663.94028 [7] Feng, Y., Fuzzy-valued mappings with finite variation, fuzzy-valued measures and fuzzy-valued Lebesgue-Stieltjes integrals, Fuzzy Sets and Systems, 121, 227-236 (2001) · Zbl 0984.28011 [8] Friedman, M.; Ming, Ma; Kandel, A., Solutions to fuzzy integral equations with arbitrary Kernels, Internat. J. Approx. Reason., 20, 246-262 (1999) · Zbl 0949.65137 [9] Gal, S. G., Approximation theory in fuzzy setting, (Anastassiou, G. A., Handbook of Analytic-Computational Methods in Applied Mathematics (2000), Chapman & Hall, CRC Press: Chapman & Hall, CRC Press Boca Raton, London, New York, Washington DC), (Chapter 13) · Zbl 0859.41030 [10] Goetschel, R.; Voxman, W., Elementary fuzzy calculus, Fuzzy Sets and Systems, 18, 31-43 (1986) · Zbl 0626.26014 [11] Lee, P. Y., Lanzhou Lectures on Henstock Integration (1989), World Scientific: World Scientific Singapore · Zbl 0699.26004 [12] Ming, M., On embedding problem of fuzzy number space, Part 4, Fuzzy Sets and Systems, 58, 185-193 (1993) [13] Wu, H.-C, Evaluate fuzzy riemann integrals using the Monte Carlo method, J. Math. Anal. Appl., 264, 324-343 (2001) · Zbl 0993.65004 [14] Wu, C.; Gong, Z., On Henstock integral of fuzzy-number-valued functions, Fuzzy Sets and Systems, 120, 523-532 (2001) · Zbl 0984.28010 [15] Wu, C.; Ming, M., On embedding problem of fuzzy number space, Part I, Fuzzy Sets and Systems, 44, 33-38 (1991) · Zbl 0757.46066 [16] Wu, C.; Ming, M., On embedding problem of fuzzy number space, Part II, 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.