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Authors: Andrzej Szymanski and Agnieszka Rossa

Affiliation: University of Lodz, Poland

Keyword(s): Mortality Models, Fuzzy Numbers, Membership Functions, Quaternion Theory.

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 H ilbert space of quaternion-valued functions as a tool for constructing the new class of mortality models. (More)

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Paper citation in several formats:
Szymanski, A., Rossa and A. (2018). The Fuzzy Mortality Model based on Quaternion Theory. In Proceedings of the 3rd International Conference on Complexity, Future Information Systems and Risk - COMPLEXIS; ISBN 978-989-758-297-4; ISSN 2184-5034, SciTePress, 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 - COMPLEXIS},
year={2018},
pages={157-165},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006813201570165},
isbn={978-989-758-297-4},
issn={2184-5034},
}

TY - CONF

JO - Proceedings of the 3rd International Conference on Complexity, Future Information Systems and Risk - COMPLEXIS
TI - The Fuzzy Mortality Model based on Quaternion Theory
SN - 978-989-758-297-4
IS - 2184-5034
AU - Szymanski, A.
AU - Rossa, A.
PY - 2018
SP - 157
EP - 165
DO - 10.5220/0006813201570165
PB - SciTePress

- Science and Technology Publications, Lda.
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