Jackson-type approximation for fuzzy-valued functions by means of trapezoidal functions

[1] G. A. Anastassiou, Fuzzy mathematics: Approximation theory, Studies in Fuzziness and Soft Computing Series,
Springer, Berlin, 2010.

[2] G. A. Anastassiou, S. G. Gal, On a fuzzy trigonometric approximation theorem of Weierstrass-type, The Journal of
Fuzzy Mathematics, 9(3) (2001), 701-708.

[3] B. Bede, S. G. Gal, Best approximation and Jackson-type estimates by generalized fuzzy polynomials, Journal of
Concrete and Applicable Mathematics, 2(3) (2004), 213-232.

[4] B. Bede, L. Stefanini, A generalization of Hukuhara di erence and division for interval and fuzzy arithmetic, Fuzzy
Sets and Systems, 230 (2013), 119-141.

[5] D. Chen, Degree of approximation by superpositions of a sigmoidal function, Approximation Theory and its Applications, 9(3) (1993), 17-28.

[6] P. Diamond, P. Kloeden, Metric spaces of fuzzy sets: Theory and applications, World Scienti c, Singapore, 1994.

[7] J. J. Font, S. Macario, Constructive approximation of continuous interval valued functions, Numerical Functional
Analysis and Optimization, 43(2) (2022), 127-144.

[8] J. J. Font, D. Sanchis, M. Sanchis, A version of the Stone-Weierstrass theorem in fuzzy analysis, Journal of Nonlinear
Sciences and Applications, 10 (2017), 4275-4283.

[9] S. G. Gal, A fuzzy variant of the Weierstrass approximation theorem, The Journal of Fuzzy Mathematics, 1(4)
(1993), 865-872.

[10] S. G. Gal, Degree of approximation of fuzzy mappings by fuzzy polynomials, The Journal of Fuzzy Mathematics,
2(4) (1994), 847-853.

[11] S. G. Gal, Approximation theory in fuzzy setting, in Handbook of Analytic-Computational Methods in Applied
Mathematics, ed. G. Anastassiou. Chapman and Hall/CRC, Boca Raton, 2000.

[12] R. Goetschel, W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986), 31-42.

[13] L. T. Gomes, L. C. Barros, A note on the generalized di erence and the generalized di erentiability, Fuzzy Sets
and Systems, 280 (2015), 142-145.

[14] B. I. Hong, N. Hahm, Approximation order to a function in C(R) by superposition of a sigmoidal function, Applied
Mathematical Letters, 15 (2002), 591-597.

[15] B. I. Hong, N. Hahm, A note on neural network approximation with a sigmoidal function, Applied Mathematical
Sciences, 10(42) (2016), 2075-2085.

[16] D. Jackson,  Uber die genauigkeit der annaherung stetiger funktionen durch ganze rationale funktionen gegebenen grades und trigonometrische summen gegebener ordnung (On the precision of the approximation of continuous functions by polynomials of given degree and by trigonometric sums of given order), Preisschrift und Dissertation, Univ. Gottingen, June 14, 1911.

[17] D. R. Jardon, M. Sanchis, Pointwise convergence topology and function spaces in fuzzy analysis, Iranian Journal
of Fuzzy Systems, 15(2) (2018), 1-21.

[18] R. I. Jewett, A variation on the Stone-Weierstrass theorem, Proceedings of the AMS - American Mathematical
Society, 14 (1963), 690-693.

[19] E. Y. Ozkan, Approximation by fuzzy (p, q)-Bernstein-Chlodowsky operators, Sahand Communications in Mathematical Analysis, 19(2) (2022), 113-132.

[20] E. Y. Ozkan, Inequalities for approximation of new de ned fuzzy post-quantum Bernstein polynomials via intervalvalued fuzzy numbers, Symmetry, 14 (2022), 696.

[21] E. Y. Ozkan, B. Hazarika, Approximation results by fuzzy Bernstein type rational functions via interval-valued
fuzzy number, Soft Computing, 27 (2023), 6893-6901.

[22] S. Panahian Fard, Z. Zainuddin, Interval type-2 fuzzy neural networks version of the Stone-Weierstrass theorem,
Neurocomputing, 74(14) (2011), 2336-2343.

[23] J. B. Prolla, On the Weierstrass-Stone theorem, Journal of Approximation Theory, 78 (1994), 299-313.

[24] L. Stefanini, A generalization of Hukuhara di erence for interval and fuzzy arithmetic, D. Dubois, M.A. Lubiano,
H. Prade, M.A. Gil, P. Grzegorzewski, O. Hryniewicz (Eds.), Soft Methods for Handling Variability and Imprecision,
Series on Advances in Soft Computing, vol. 48, Springer (2008), An extended version is available online at the RePEc
service: http://econpapers.repec.org/RAS/pst233.htm.

[25] L. Stefanini, A generalization of Hukuhara di erence and division for interval and fuzzy arithmetic, Fuzzy Sets and
Systems, 161 (2010), 1564-1584.

[26] Y. R. Syau, E. S. Lee, Fuzzy Weirstrass theorem and convex fuzzy mappings, Computers and Mathematics with
Applications, 51 (2006), 1741-1750.

[27] J. Szabados, On a problem of R. DeVore, Acta Mathematica Hungarica, 27(1-2) (1976), 219-223.