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In the paper, a stochastic hybrid mortality model (EHLC) treated as a solution of stochastic differential equations is introduced. The model is defined analogously to the well-known Lee-Carter mortality model (LC). A parameter estimation procedure including a switching rule are proposed. A comparison of the predictive accuracy of the LC and EHLC models based on the mortality data for Poland has shown that the new model yields better results.

The new trends in fuzzy analysis are based on the algebraic approach to fuzzy numbers. The essential idea in such an approach is representing the membership function of a fuzzy number as an element of any square‐integrable function space. As a starting point, we consider the Koissi–Shapiro model known as a fuzzy version of the Lee–Carter mortality model, in which triangular membership functions of fuzzy variables are assumed. In our approach, the algebra of ordered fuzzy numbers is used to reformulate the fuzzy Lee–Carter mortality model and to improve the prediction accuracy.

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Parity progression ratios (PPR's) have been extensively described in literature on demography and have played an important role in fertility, unlike the idea of calculating projected parity progression ratios proposed by Brass (1985). However, we decided to use this method in our paper to analyse future fertility trends, firstly by assessing age-specific parity progression ratios for women in childbearing ages, and then by comparing these ratios with ratios at the end of women's reproductive life, as well as by comparing the latter with the completed PPR's. More specifically, the aim of this study is to adopt a modified Brass method to calculate the projected parity progression ratios using the age-period fertility data sourced from the Human Fertility Database (HFD). We progress to use the observed and predicted age-specific PPR's to examine parity progressions in Poland as a case study.