Trapezoidal operator preserving the expected interval and the support of fuzzy numbers

Authors

  • Adriana Brândaş Babeş-Bolyai University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat401-948

Keywords:

fuzzy number, trapezoidal fuzzy number, trapezoidal approximation
Abstract views: 208

Abstract

The problem to find the trapezoidal fuzzy number which preserves the expected interval and the support of a given fuzzy number is discussed. Properties of this new trapezoidal approximation operator are studied.

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References

Allahviranloo, T. and Adabitabar Firozja, M., Note on trapezoidal approximation of fuzzy numbers, Fuzzy Sets and Systems, 158, pp. 755-756, 2007, https://doi.org/10.1016/j.fss.2006.10.017 DOI: https://doi.org/10.1016/j.fss.2006.10.017

Ban, A., Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected value, Fuzzy Sets and Systems, 159, pp. 1327-1344, 2008, https://doi.org/10.1016/j.fss.2007.09.008 DOI: https://doi.org/10.1016/j.fss.2007.09.008

Ban, A., Triangular and parametric approximations of fuzzy numbers-inadvertences and corrections, Fuzzy Sets and Systems, 160, pp. 3048-3058, 2009, https://doi.org/10.1016/j.fss.2009.04.003 DOI: https://doi.org/10.1016/j.fss.2009.04.003

Ban, A., On the nearest parametric approximation of a fuzzy number - Revisited, Fuzzy Sets and Systems, 160, pp. 3027-3047, 2009, https://doi.org/10.1016/j.fss.2009.05.001 DOI: https://doi.org/10.1016/j.fss.2009.05.001

Bodjanova, S., Median value interval of a fuzzy number, Information Sciences, 172, pp. 73-89, 2005, https://doi.org/10.1016/j.ins.2004.07.018 DOI: https://doi.org/10.1016/j.ins.2004.07.018

Chanas, S., On the interval approximation of a fuzzy number, Fuzzy Sets and Systems, 122, pp. 353-356, 2001, https://doi.org/10.1016/s0165-0114(00)00080-4 DOI: https://doi.org/10.1016/S0165-0114(00)00080-4

Delgado, M., Vila, M. A. and Voxman, W., On a canonical representation of fuzzy numbers, Fuzzy Sets and Systems, 93, pp. 125-135, 1998, https://doi.org/10.1016/s0165-0114(96)00144-3 DOI: https://doi.org/10.1016/S0165-0114(96)00144-3

Diamond, P. and Kloeden, P., Metric Spaces of Fuzzy Sets. Theory and Applications, World Scientific, Singapore 1994. DOI: https://doi.org/10.1142/2326

Dubois, D. and Prade, H., Operations on fuzzy numbers, Internat. J. Systems Sci, 9, pp. 613-626, 1978, https://doi.org/10.1080/00207727808941724 DOI: https://doi.org/10.1080/00207727808941724

Dubois, D. and Prade, H., The mean value of a fuzzy number, Fuzzy Sets and Systems, 24, pp. 279-300, 1987, https://doi.org/10.1016/0165-0114(87)90028-5 DOI: https://doi.org/10.1016/0165-0114(87)90028-5

Grzegorzewski, P., Metrics and orders of fuzzy numbers, Fuzzy Sets and Systems, 97, pp. 83-94, 1998. https://doi.org/10.1016/s0165-0114(96)00322-3 DOI: https://doi.org/10.1016/S0165-0114(96)00322-3

Grzegorzewski, P. and Mrowka, E., Trapezoidal approximations of fuzzy numbers, Fuzzy Sets and Systems, 153, pp. 115-135, 2005, https://doi.org/10.1016/j.fss.2004.02.015 DOI: https://doi.org/10.1016/j.fss.2004.02.015

Grzegorzewski, P. and Mrowka, E., Trapezoidal approximations of fuzzy numbers - revisited, Fuzzy Sets and Systems, 158, pp. 757-768, 2007, https://doi.org/10.1016/j.fss.2006.11.015 DOI: https://doi.org/10.1016/j.fss.2006.11.015

Guerra, M. L. and Stefanini, L., Approximate fuzzy arithmetic operations using monotonic interpolations, Fuzzy Sets and Systems, 150, pp. 5-33, 2005, https://doi.org/10.1016/j.fss.2004.06.007 DOI: https://doi.org/10.1016/j.fss.2004.06.007

Heilpern, S., The expected value of a fuzzy number, Fuzzy Sets and Systems, 47, pp. 81-86, 1992, https://doi.org/10.1016/0165-0114(92)90062-9 DOI: https://doi.org/10.1016/0165-0114(92)90062-9

Hung, W. and Hu, J., A note on the correlation of fuzzy numbers by expected interval, Internat. J. Uncertainty Fuzziness and Knowledge-based System, 9, pp. 517-523, 2001, https://doi.org/10.1016/s0218-4885(01)00092-2 DOI: https://doi.org/10.1142/S0218488501000922

Jimenez, M., Ranking fuzzy numbers through of its expected interval, Internat. J. Uncertainty Fuzziness and Knowledge-based System, 4, pp. 379-388, 1996, https://doi.org/10.1142/s0218488596000226 DOI: https://doi.org/10.1142/S0218488596000226

Nasibov, E. N. and Peker, S., On the nearest parametric approximation of a fuzzy number, Fuzzy Sets and Systems, 159, pp. 1365-1375, 2008, https://doi.org/10.1016/j.fss.2007.08.005 DOI: https://doi.org/10.1016/j.fss.2007.08.005

Yager, R. R., A procedure for ordering fuzzy subset of the unit interval, IInformation Sciences, 24, pp. 143-161, 1981, https://doi.org/10.1016/0020-0255(81)90017-7 DOI: https://doi.org/10.1016/0020-0255(81)90017-7

Yeh, C.-T., A note on trapezoidal approximation of fuzzy numbers, Fuzzy Sets and Systems, 158, pp. 747-754, 2007, https://doi.org/10.1016/j.fss.2006.11.017 DOI: https://doi.org/10.1016/j.fss.2006.11.017

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Published

2011-02-01

How to Cite

Brândaş, A. (2011). Trapezoidal operator preserving the expected interval and the support of fuzzy numbers. Rev. Anal. Numér. Théor. Approx., 40(1), 24–37. https://doi.org/10.33993/jnaat401-948

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