Abstract: The mortality models are of fundamental importance in many areas, such as the pension plans, the care of the elderly, the provision of health service, etc. In the paper we propose a new class of mortality models based on a fuzzy version of the well-known
Lee–Carter model (1992). Theoretical backgrounds are based on the algebraic approach to fuzzy numbers. The essential idea in our approach focuses on representing a membership function of a fuzzy number as an element of C*-Banach algebra.
If the membership function µ(z) of a fuzzy number is strictly monotonic on two disjoint intervals, then it can be decomposed into strictly decreasing and strictly increasing functions, and the inverse functions f(u), g(u) can be found.
The membership function µ(z) can be represented by means of a complex-valued function f(u) + ig(u), where i is an imaginary unit. Then the pair (f, g) is a quaternion and quaternion-valued square integrable functions form the separable Hilbert space.
We use the Hilbert space of quaternion-valued functions as a tool for constructing the new class of mortality models.(More)

The mortality models are of fundamental importance in many areas, such as the pension plans, the care of the elderly, the provision of health service, etc. In the paper we propose a new class of mortality models based on a fuzzy version of the well-known Lee–Carter model (1992). Theoretical backgrounds are based on the algebraic approach to fuzzy numbers. The essential idea in our approach focuses on representing a membership function of a fuzzy number as an element of C*-Banach algebra. If the membership function µ(z) of a fuzzy number is strictly monotonic on two disjoint intervals, then it can be decomposed into strictly decreasing and strictly increasing functions, and the inverse functions f(u), g(u) can be found. The membership function µ(z) can be represented by means of a complex-valued function f(u) + ig(u), where i is an imaginary unit. Then the pair (f, g) is a quaternion and quaternion-valued square integrable functions form the separable Hilbert space. We use the Hilbert space of quaternion-valued functions as a tool for constructing the new class of mortality models.

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Szymanski, A. and Rossa, A. (2018). The Fuzzy Mortality Model based on Quaternion Theory.In Proceedings of the 3rd International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS, ISBN 978-989-758-297-4, pages 157-165. DOI: 10.5220/0006813201570165

@conference{complexis18, author={Andrzej Szymanski. and Agnieszka Rossa.}, title={The Fuzzy Mortality Model based on Quaternion Theory}, booktitle={Proceedings of the 3rd International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,}, year={2018}, pages={157-165}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0006813201570165}, isbn={978-989-758-297-4}, }

TY - CONF

JO - Proceedings of the 3rd International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS, TI - The Fuzzy Mortality Model based on Quaternion Theory SN - 978-989-758-297-4 AU - Szymanski, A. AU - Rossa, A. PY - 2018 SP - 157 EP - 165 DO - 10.5220/0006813201570165