Width invariant approximation of fuzzy numbers

[1] S. Abbasbandy and M. Amirfakhrian, The nearest approximation of a fuzzy quantity in
parametric form, Applied Mathematics and Computation, 172 (2006), 624–632.
[2] S. Abbasbandy and M. Amirfakhrian, The nearest trapezoidal form of a generalized left right
fuzzy number, International Journal of Approximate Reasoning, 43 (2006), 166–178.
[3] S. Abbasbandy and B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity,
Applied Mathematics and Computation, 156 (2004), 381–386.
[4] S. Abbasbandy and T. Hajjari, Weighted trapezoidal approximation-preserving core of a fuzzy
number, Computers and Mathematics with Applications, 59 (2010),3066–3077.
[5] T. Allahviranloo and M. Adabitabar Firozja, Note on "Trapezoidal approximation of fuzzy
numbers", Fuzzy Sets and Systems, 158 (2007), 755–756.
[6] A. I. Ban, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the
expected interval, Fuzzy Sets and Systems, 159 (2008), 1327-1344.
[7] A. I. Ban, Trapezoidal and triangular approximations of fuzzy numbers-inadvertences and
corrections, Fuzzy Sets and Systems, 160 (2009), 3048-3058.
[8] A. I. Ban, A. Brandas, L. Coroianu, C. Negrutiu and O. Nica, Approximations of fuzzy
numbers by trapezoidal fuzzy numbers preserving the ambiguity and value, Computers and
Mathematics with Applications, 61 (2011), 1379-1401.
[9] A. I. Ban and L. Coroianu, Translation invariance and scale invariance of approximations of
fuzzy numbers, in: 7th Conference of the European Society for Fuzzy Logic and Technology,
Aix-Les-Bains, 18-22 July 2011.
[10] A. I. Ban and L. Coroianu, Nearest interval, triangular and trapezoidal approximation of
a fuzzy number preserving ambiguity, International Journal of Approximate Reasoning, 53
(2012), 805–836.
[11] A.I. Ban, L. Coroianu, Existence, uniqueness and continuity of trapezoidal approximations
of fuzzy numbers under a general condition, Fuzzy Sets and Systems, 257(2014), 3-22.
[12] A. Brandas, Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the
core, the ambiguity and the value, Advanced Studies in Contemporary Mathematics, 21
(2011), 247259.
[13] S. Bodjanova, Median value and median interval of a fuzzy number, Information Sciences,
172 (2005), 73-89.
[14] S. Chanas, On the interval approximation of a fuzzy number, Fuzzy Sets and Systems, 122
(2001), 353-356.
[15] L. Coroianu, M. Gagolewski and P. Grzegorzewski, Nearset piecewise linear approximation
of fuzzy numbers, Fuzzy Sets and Systems, 233 (2013), 26-51.
[16] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, theory and applications, World
Scientific, Singapore, 1994.
[17] D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci., 30 (1978), 613-626.
[18] D. Dubois, H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems, 24 (1987),
279-300.
[19] P. Grzegorzewski, Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems, 97
(1998), 83-94.
[20] P. Grzegorzewski, Nearest interval approximation of a fuzzy number, Fuzzy Sets and Systems,
130 (2002), 321-330.
[21] P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers, Fuzzy Sets and
Systems, 153 (2005), 115-135.
[22] P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers-revisited, Fuzzy
Sets and Systems, 158 (2007), 757-768.
[23] S. Heilpern, The expected value of a fuzzy number, Fuzzy Sets and Systems, 47 (1992) 81-86.
[24] W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1986.
[25] C. T. Yeh, A note on trapezoidal approximation of fuzzy numbers, Fuzzy Sets and Systems,
158 (2007), 747-754.

[26] C. T. Yeh, On improving trapezoidal and triangular approximations of fuzzy numbers, International
Journal of Approximate Reasoning, 48 (2008), 297-313.
[27] C. T. Yeh, Trapezoidal and triangular approximations preserving the expected interval, Fuzzy
Sets and Systems, 159 (2008), 1345–1353.
[28] C. T. Yeh, Weighted trapezoidal and triangular approximations of fuzzy numbers, Fuzzy Sets
and Systems, 160 (2009), 3059–3079.
[29] C. T. Yeh, Weighted semi-trapezoidal approximations of fuzzy numbers, Fuzzy Sets and Systems,
165 (2011), 61-80.
[30] C. T. Yeh, H. M. Chu, Approximations by LR-type fuzzy numbers, Fuzzy Sets and Systems,
257 (2014) 23-40.
[31] W. Zeng, H. Li, Weighted triangular approximation of fuzzy numbers, International Journal
of Approximate Reasoning, 46 (2007), 137–150.