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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).

MSC:

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

[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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