[1] |
Bartkowiak, M., & Rutkowska, A. (2018). Fuzzy approaches in forecasting mortality rates. In J.Kacprzyk (ed.), E.Szmidt (ed.), S.Zadrożny (ed.), K.Atanassov (ed.), & M.Krawczak (ed.) (Eds.), Advances in Fuzzy Logic and Technology 2017, 996, Proceedings of EUSFLAT‐2017 - The 10th Conference of the European Society for Fuzzy Logic and Technology, September 11-15, 2017, Warsaw, Poland and IWIFSGN’2017 - The Sixteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, September 13-15, 2017, Warsaw, Poland, Volume 1 Springer, Cham. |
[2] |
Bongaarts, J. (2005). Long‐range trends in adult mortality: Models and projection methods. Demography, 42(1), 23-49. |
[3] |
Booth, H., Hyndman, R. J., Tickle, L., & De Jong, P. (2006). Lee‐Carter mortality forecasting: A multi‐country comparison of variants and extensions models. Demographic Research, 15(9), 289-310. |
[4] |
Brouhns, N., Denuit, M., & Vermunt, J. K. (2002). A Poisson log‐bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373-393. · Zbl 1074.62524 |
[5] |
Cairns, A. J. G., Blake, D., & Dowd, K. (2006). A two‐factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73, 687-718. |
[6] |
Currie, I. D., Durban, M., & Eilers, P. H. C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4(4), 279-298. · Zbl 1061.62171 |
[7] |
Danesi, I. L., Haberman, S., & Millossovich, P. (2015). Forecasting mortality in subpopulations using Lee‐Carter type models: A comparison. Insurance: Mathematics and Economics, 62(4), 151-161. · Zbl 1318.91109 |
[8] |
De Andrés‐Sánchez, J., & Puchades, L. G.‐V. (2019). A fuzzy‐random extension of the Lee‐Carter mortality prediction model. International Journal of Computational Intelligence Systems, 12(2), 775-794. |
[9] |
De Jong, P., & Tickle, L. (2006). Extending Lee-Carter mortality forecasting. Mathematical Population Studies, 13(1), 1-18. · Zbl 1151.91742 |
[10] |
Demirel, D. F., & Basak, M. (2015). A modified fuzzy Lee‐Carter method for modeling human mortality. In A.Rosa (ed.), J. J.Merelo (ed.), A.Dourado (ed.), J. M.Cadenas (ed.), K.Madani (ed.), A.Ruano (ed.), & J.Filipe (ed.) (Eds.), Proceedings of the 7th International Joint Conference on Computational Intelligence (pp. 17-24). Lisbon, SciTePress - Science and Technology Publications, Lda, https://www.scitepress.org/ProceedingsDetails.aspx?ID=RCZ7WUIPfKk=&t=1. |
[11] |
Diamond, P. (1988). Fuzzy least‐squares. Information Sciences, 46(3), 141-157. · Zbl 0663.65150 |
[12] |
Dubois, D., & Prade, H. (1978). Operations on fuzzy numbers. International Journal of Systems Science, 9(6), 613-626. · Zbl 0383.94045 |
[13] |
Haberman, S., & Renshaw, A. (2012). Parametric mortality improvement rate modelling and projecting. Insurance: Mathematics and Economics, 50(3), 309-333. · Zbl 1237.91129 |
[14] |
Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Retrieved from https://www.mortality.org;https://www.humanmortality.de. |
[15] |
Koissi, M.‐C., & Shapiro, A. F. (2006). Fuzzy formulation of the Lee‐Carter model for mortality forecasting. Insurance: Mathematics and Economics, 39, 287-309. · Zbl 1151.91576 |
[16] |
Kosiński, W. (2006). On fuzzy number calculus. International Journal of Applied Mathematics and Computer Science, 16(1), 51-57. · Zbl 1334.94112 |
[17] |
Kosiński, W., & Prokopowicz, P. (2004). Algebra of fuzzy numbers. Matematyka Stosowana. Matematyka dla Społeczeństwa, 5(46), 37-63 (in Polish). |
[18] |
Kosiński, W., Prokopowicz, P., & Ślęzak, D. (2002a). Drawback of fuzzy arthmetics—New intutions and propositions. In T.Burczynski (ed.), W.Cholewa (ed.), & W.Moczulski (ed.) (Eds.), Proceedings of Methods of Artificial Intelligence (pp. 231-237). Gliwice: PACM. |
[19] |
Kosiński, W., Prokopowicz, P., & Ślęzak, D. (2002b). Fuzzy numbers with algebraic operations: Algorithmic approach. In M.Klopotek (ed.), S. T.Wierzchoń (ed.), & M.Michalewicz (ed.) (Eds.), Intelligent Information Systems 2002, Advances in Soft Computing (Vol. 17, pp. 311-320). Heidelberg: Physica Verlag. https://doi.org/10.1007/978-3-7908-1777-5_33. · doi:10.1007/978-3-7908-1777-5_33 |
[20] |
Kosiński, W., Prokopowicz, P., & Ślęzak, D. (2003). Ordered fuzzy numbers. Bulletin of the Polish Academy of Sciences Mathematics, 51, 327-338. |
[21] |
Kou, Y. (2016). Fuzzy formulation of the Lee‐Carter model for the mortality forecasting with age‐specific enhancement. In B.‐Y.Cao (ed.), P.‐Z.Wang (ed.), Z.‐L.Liu (ed.), & Y.‐B.Zhong (ed.) (Eds.), International Conference on Oriental Thinking and Fuzzy Logic (pp. 177-196). Switzerland: Springer International Publishing. |
[22] |
Lee, R. D., & Carter, L. (1992). Modeling and forecasting the time series of U.S. mortality. Journal of the American Statistical Association, 87, 659-671. · Zbl 1351.62186 |
[23] |
Marszałek, A., & Burczyński, T. (2013). Financial fuzzy time series models based on ordered fuzzy numbers. In W.Pedrycz (ed.) & S.‐M.Chen (ed.) (Eds.), Time Series Analysis, Modelling and Applications (pp. 77-95). Berlin: Springer. |
[24] |
Marszałek, A., & Burczyński, T. (2014). Modeling and forecasting financial time series with ordered fuzzy candlesticks. Information Sciences, 273, 144-155. · Zbl 1414.91425 |
[25] |
Pitacco, E., Denuit, M., Haberman, S., & Olivieri, A. (2009). Modelling Longevity Dynamics for Pensions and Annnuity Business. Oxford University Press, New York, https://www.amazon.com/Modelling-Longevity-Dynamics-Pensions-Mathematics/dp/0199547270#reader_0199547270. · Zbl 1163.91005 |
[26] |
Prokopowicz, P., & Ślȩzak, D. (2017). Ordered fuzzy numbers: Definitions and operations. In P.Prokopowicz (ed.), J.Czerniak (ed.), D.Mikolajewski (ed.), L.Apiecionek (ed.), & D.Ślȩzak (ed.) (Eds.), Theory and Applications of Ordered Fuzzy Numbers. Studies in Fuzziness and Soft Computing (Vol. 356, pp. 57-79). Cham: Springer. · Zbl 1392.03006 |
[27] |
Renshaw, A. E., & Haberman, S. (2003). Lee‐Carter mortality forecasting with age specific enhancement. Insurance: Mathematics and Economics, 33(2), 255-272. · Zbl 1103.91371 |
[28] |
Renshaw, A., Haberman, S., & Hatzopoulos, P. (1996). The modelling of recent mortality trends in United Kingdom male assured lives. British Actuarial Journal, 2, 449-477. |
[29] |
Rossa, A., Socha, L., & Szymański, A. (2017). Hybrid Dynamic and Fuzzy Models of Mortality. University of Lodz Press, Lodz. |
[30] |
Szymański, A., & Rossa, A. (2014). Fuzzy mortality model based on Banach algebra. International Journal of Intelligent Technologies and Applied Statistics, 7, 241-265. |
[31] |
Szymański, A., & Rossa, A. (2017). Improvement of fuzzy mortality model by means of algebraic methods. Statistics in Transition, 18, 701-724. |
[32] |
Tuljapurkar, S., Li, N., & Boe, C. (2000). A universal pattern of mortality decline in the G7 countries. Nature, 405, 789-792. |
[33] |
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. · Zbl 0139.24606 |