Abstract
Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. New algorithms for calculating the proper approximations are proposed. It is shown that the adequate approximation operator is chosen with respect both to the global spread of a fuzzy number and the size of possible asymmetry between the spread of the left-hand and right-hand part of a fuzzy number.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Abbasbandy, S., Asady, B.: The nearest approximation of a fuzzy quantity in parametric form. Applied Mathematics and Computation 172, 624–632 (2006)
Abbasbandy, S., Amirfakhrian, M.: The nearest trapezoidal form of a generalized LR fuzzy number. International Journal of Approximate Reasoning 43, 166–178 (2006)
Allahviranloo, T., Firozja, M.A.: Note on trapezoidal approximations of fuzzy numbers. Fuzzy Sets and Systems 158, 755–756 (2007)
Ban, A.: Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval. Fuzzy Sets and Systems 159, 1327–1344 (2008)
Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers. Mathware and Soft Computing 2, 71–84 (1995)
Chanas, S.: On the interval approximation of a fuzzy number. Fuzzy Sets and Systems 122, 353–356 (2001)
Delgado, M., Vila, M.A., Voxman, W.: On a canonical representation of a fuzzy number. Fuzzy Sets and Systems 93, 125–135 (1998)
Delgado, M., Vila, M.A., Voxman, W.: A fuzziness measure for fuzzy number: applications. Fuzzy Sets and Systems 94, 205–216 (1998)
Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9, 613–626 (1978)
Dubois, D., Prade, H.: The mean value of a fuzzy number. Fuzzy Sets and Systems 24, 279–300 (1987)
Grzegorzewski, P.: Metrics and orders in space of fuzzy numbers. Fuzzy Sets and Systems 97, 83–94 (1998)
Grzegorzewski, P.: Nearest interval approximation of a fuzzy number. Fuzzy Sets and Systems 130, 321–330 (2002)
Grzegorzewski, P.: Approximation of a Fuzzy Number Preserving Entropy-Like Nonspecifity. Operations Research and Decisions 4, 49–59 (2003)
Grzegorzewski, P.: Trapezoidal approximations of fuzzy numbers preserving the expected interval - algorithms and properties. Fuzzy Sets and Systems 159, 1354–1364 (2008)
Grzegorzewski, P.: New algorithms for trapezoidal approximation of fuzzy numbers preserving the expected interval. In: Magdalena, L., Ojeda-Aciego, M., Verdegay, J.L. (eds.) Proceedings of the Twelfth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2008, Spain, Torremolinos, Málaga, June 22-27, pp. 117–123 (2008)
Grzegorzewski, P., Mrówka, E.: Trapezoidal approximations of fuzzy numbers. Fuzzy Sets and Systems 153, 115–135 (2005)
Grzegorzewski, P., Mrówka, E.: Trapezoidal approximations of fuzzy numbers - revisited. Fuzzy Sets and Systems 158, 757–768 (2007)
Grzegorzewski, P., Pasternak-Winiarska, K.: Weighted trapezoidal approximations of fuzzy numbers. In: Proceedings of IFSA World congress and Eusflat Conference IFSA/Eusflat 2009, Lisbon, Portugal, July 20-24, pp. 1531–1534 (2009)
Grzegorzewski, P., Stefanini, L.: Non-linear shaped approximation of fuzzy numbers. In: Proceedings of IFSA World congress and Eusflat Conference IFSA/Eusflat 2009, Lisbon, Portugal, July 20-24, pp. 1535–1540 (2009)
Heilpern, S.: The expected value of a fuzzy number. Fuzzy Sets and Systems 47, 81–86 (1992)
Wang, Y.M., Yang, J.B., Xu, D.L., Chin, K.S.: On the centroids of fuzzy numbers. Fuzzy Sets and Systems 157, 919–926 (2006)
Yeh, C.T.: A note on trapezoidal approximations of fuzzy numbers. Fuzzy Sets and Systems 158, 747–754 (2007)
Yeh, C.T.: Trapezoidal and triangular approximations preserving the expected interval. Fuzzy Sets and Systems 159, 1345–1353 (2008)
Yeh, C.T.: On improving trapezoidal and triangular approximations of fuzzy numbers. International Journal of Approximate Reasoning 48, 297–313 (2008)
Zeng, W., Li, H.: Weighted triangular approximation of fuzzy numbers. International Journal of Approximate Reasoning 46, 137–150 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Grzegorzewski, P. (2010). Algorithms for Trapezoidal Approximations of Fuzzy Numbers Preserving the Expected Interval. In: Bouchon-Meunier, B., Magdalena, L., Ojeda-Aciego, M., Verdegay, JL., Yager, R.R. (eds) Foundations of Reasoning under Uncertainty. Studies in Fuzziness and Soft Computing, vol 249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10728-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-10728-3_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10726-9
Online ISBN: 978-3-642-10728-3
eBook Packages: EngineeringEngineering (R0)