Possibilistic moment generating functions. (English) Zbl 1214.03042

Summary: Following C. Carlsson and R. Fullér [Fuzzy Sets Syst. 122, No. 2, 315–326 (2001; Zbl 1016.94047)], the authors [Math. Comput. Modelling 49, No. 1–2, 352–368 (2009; Zbl 1165.91414)] have recently introduced higher-order weighted possibilistic moments of fuzzy numbers. In this paper, we define the weighted possibilistic moment generating functions (MGF) of fuzzy numbers and obtain the closed-form expressions for triangular, trapezoidal and parabolic fuzzy numbers. Applications involve derivation of higher-order possibilistic moments of volatility models (see the authors’ paper cited above for details).


03E72 Theory of fuzzy sets, etc.
26E50 Fuzzy real analysis
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text: DOI


[1] Thavaneswaran, A.; Appadoo, S. S.; Paseka, A., Weighted possibilistic moments of fuzzy numbers with applications to GARCH modeling and option pricing, Mathematical and Computer Modelling, 49, 352-368 (2009) · Zbl 1165.91414
[2] Carlsson, C.; Fuller, R., On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems, 122, 315-326 (2001) · Zbl 1016.94047
[3] Zimmermann, H. J., Fuzzy Sets Theory and its Applications (2001), Kluwer Academic Publishers: Kluwer Academic Publishers Nowell, MA, USA · Zbl 0969.54002
[4] Grzegorzewski, P.; Mrowka, E., Trapezoidal approximations of fuzzy numbers-revisited, Fuzzy Sets and Systems, 158, 757-768 (2007) · Zbl 1119.03052
[5] Saeidifar, A.; Pasha, E., The possibilistic moments of fuzzy numbers and their applications, Journal of Computational and Applied Mathematics, 223, 1028-1042 (2009) · Zbl 1159.65013
[6] Thiagarajah, K.; Thavaneswaran, A., Fuzzy random coefficient volatility models with financial applications, The Journal of Risk Finance, 7, 503-524 (2006)
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