The Complex-Number Mortality Model (CNMM) based on orthonormal expansion of membership functions

Andrzej Szymański; Agnieszka Rossa

doi:10.21307/stattrans-2021-026

The Complex-Number Mortality Model (CNMM) based on orthonormal expansion of membership functions

Andrzej Szymański Institute of Statistics and Demography, University of Lodz, 41 Rewolucji 1905 St., 90-214 Lodz, Poland , Agnieszka Rossa Institute of Statistics and Demography, University of Lodz, 41 Rewolucji 1905 St., 90-214 Lodz, Poland ORCID:https://orcid.org/0000-0002-0444-4181 Statistics in Transition new series, vol. 22, 2021, 3, pages: 31–57 Published online: 6 September 2021 DOI 10.21307/stattrans-2021-026

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ABSTRACT

The paper deals with a new fuzzy version of the Lee-Carter (LC) mortality model, in which mortality rates as well as parameters of the LC model are treated as triangular fuzzy numbers. As a starting point, the fuzzy Koissi-Shapiro (KS) approach is recalled. Based on this approach, a new fuzzy mortality model – CNMM – is formulated using orthonormal expansions of the inverse exponential membership functions of the model components. The paper includes numerical findings based on a case study with the use of the new mortality model compared to the results obtained with the standard LC model.

KEYWORDS

exponential membership functions, Legendre’s polynomials, mortality modelling, orthonormal system

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