Abstract
The problem of the trapezoidal approximation of fuzzy numbers is discussed. A set of criteria for approximation operators is formulated. A new nearest trapezoidal approximation operator preserving expected interval is suggested.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chanas S., On the interval approximation of a fuzzy number, Fuzzy Sets and Systems 122 (2001), 353–356.
Dubois D., Prade H., Operations on fuzzy numbers, Int. J. Syst. Sci. 9 (1978), 613–626.
Dubois D., Prade H., The mean value of a fuzzy number, Fuzzy Sets and Systems 24 (1987), 279–300.
Grzegorzewski P., Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems 97 (1998), 83–94.
Grzegorzewski P., Interval approximation of a fuzzy number and the principle of information invariance, In: Proceedings of the 9th International Conference on Information Processing and Management of Uncertainty IPMU’2002, Annecy, 1–5 July 2002, pp. 347–354.
Grzegorzewski P., Nearest interval approximation of a fuzzy number, Fuzzy Sets and Systems 130 (2002), 321–330.
Heilpern S., The expected value of a fuzzy number, Fuzzy Sets and Systems 47 (1992), 81–86.
Hung W., Wu J., A note on the correlation of fuzzy numbers by expected interval, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9 (2001), 517–523.
Jimenez M., Ranking fuzzy numbers through the comaparison of its expected intervals, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 4 (1996), 379–388.
Jimenez M., Rivas J.A., Fuzzy number approximation, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 6 (1998), 68–78.
van Leewijck W., Kerre E.E., Defuzzification: criteria and classification, Fuzzy Sets and Systems 108 (1999), 159–178.
Runkler T.A., Glesner M., A set of axioms for defuzzification strategies — towards a theory of rational defuzzification operators, in: Proc. 2nd IEEE Internat. Conf. on Fuzzy Systems, San Francisco, 1993, pp. 1161–1166.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Grzegorzewski, P., Mrówka, E. (2003). Trapezoidal Approximations of Fuzzy Numbers. In: Bilgiç, T., De Baets, B., Kaynak, O. (eds) Fuzzy Sets and Systems — IFSA 2003. IFSA 2003. Lecture Notes in Computer Science, vol 2715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44967-1_28
Download citation
DOI: https://doi.org/10.1007/3-540-44967-1_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40383-8
Online ISBN: 978-3-540-44967-6
eBook Packages: Springer Book Archive