Well-being horizons for silver and golden ages: an application of traditional and fuzzy Markov chains

European societies are currently in a process of population ageing. Although this is the general trend, it would be desirable to know whether the characteristics and intensity of this ageing process are homogeneous in all European countries. In this work, information coming from three macro-surveys (or waves) of the Survey on Health Ageing and Retirement in Europe is used for Denmark, Germany, Poland and Spain, as the basis for a longitudinal well-being and dependency indicator with the aim of studying whether the characteristics of ageing are similar in these regions. First, long-term population distributions are obtained according to the scores of the aforementioned indicator. Next, classical and fuzzy Markov chains are used to estimate steady-state distributions regarding age group, gender, country and wave. Finally, by means of a proper metric for probability distributions, steady-state distributions are clustered in different profiles, which leads us to conclude that the ageing process is not homogeneous among the studied populations.