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In the paper a new class of fuzzy mortality models based on a fuzzy version of the well-known Lee-Carter model is proposed. We applied the algebra of quaternions to describe fuzzy mortality models. It can be easily seen that the quaternion algebra, with a proper definition of multiplication, is a non-commutative C*-Banach algebra. Therefore, we can use  the C*-Banach algebra and the von Neumann algebra to describe fuzzy models in the terms of the non-commutative C*-Banach algebras.  Thus, in our approach the membership functions of fuzzy model parameters are represented by quaternions. The main objective is estimation of such functions. In the paper some estimation results based on real data are presented and discussed.

fuzzy mortality model, C*-Banach algebra, non-commutative C*-algebra, von Neumann algebra of projectors, quaternion algebra