Fuzzy Approaches in Forecasting Mortality Rates

  • Marcin Bartkowiak
  • Aleksandra RutkowskaEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)


Fundamental issues in the study of mortality rate modelling are goodness of fit and the quality of forecasts. These are still open questions despite the fact that dozens of mortality models have been formulated. Capturing all mortality patterns remains elusive for the proposed models. Nevertheless, there are models with better and worse abilities to explain historical mortality rates and to project accurate forecasts. This paper considers two fuzzy approaches for forecasting future mortality rates. First, the fuzzy autoregressive integrated moving average (ARIMA) method allows the making of fuzzy forecasts based on crisp estimates of mortality model parameters. Second, the fuzzy Lee-Carter method models past mortality rates as fuzzy numbers, and then allows the prediction of future fuzzy mortality rates. Numerical findings show that both methods may be useful tools for forecasting.


Mortality rate Lee-Carter model Fuzzy ARIMA Mortality forecasting 


  1. 1.
    Box, G.E., Jenkins G.M.: Time Series Analysis: Forecasting and Control, revised edn. Holden-Day (1976)Google Scholar
  2. 2.
    Cairns, A.J.G., et al.: A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North Am. Actuarial J. 13(1), 1–35 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Haberman, S., Renshaw, A.: A comparative study of parametric mortality projection models. Insur.: Math. Econ. 48(1), 35–55 (2011)MathSciNetGoogle Scholar
  4. 4.
    Hyndman, R.J., Athanasopoulos, G.: Forecasting: Principles and Practice. OTexts (2014)Google Scholar
  5. 5.
    Hong, D.H., Hae, Y.D.: Fuzzy system reliability analysis by the use of T (the weakest t-norm) on fuzzy number arithmetic operations. Fuzzy Sets Syst. 90(3), 307–316 (1997)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Kolesárová, A.: Triangular norm-based addition preserving linearity of T-sums of linear fuzzy intervals. Mathware Soft Comput. 5(1), 1998 (1998)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Kosiński, W., Prokopowicz, P., Ślȩzak, D.: Ordered fuzzy numbers. Bull. Pol. Acad. Sci., Ser. Sci. Math 51(3), 327–338 (2003)Google Scholar
  8. 8.
    Koissi, M.-C., Shapiro, A.F.: Fuzzy formulation of the Lee Carter model for mortality forecasting. Insur.: Math. Econ. 39(3), 287–309 (2006)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Lee, R.D., Carter, L.R.: Modeling and forecasting US mortality. J. Am. Stat. Assoc. 87(419), 659–671 (1992)zbMATHGoogle Scholar
  10. 10.
    Szymański, A., Rossa, A.: Fuzzy mortality model based on Banach algebra. Int. J. Intell. Technol. Appl. Stat. 7(3), 241–265 (2014)Google Scholar
  11. 11.
    Tseng, F.-M., et al.: Fuzzy ARIMA model for forecasting the foreign exchange market. Fuzzy Sets Syst. 118(1), 9–19 (2001)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Poznan University of Economics and BusinessPoznanPoland

Personalised recommendations