Classifications with relations. I. A model for the description of distributions and their distances

Distributions on classifications are met wherever we work with categorical variables. A vast investigation has been done in developing methods for statistical analysis of nominal variables (e.g. variables with simple classification), partially are solved also problems for ordered classifications and classifications with assigned numbers. In this paper we propose a general model which enables us to develop descriptive measures for distributions on various types of classifications with relations. The simple, ordered and quantitative classifications will be special cases of this general model. In this way, it is possible to handle with general decision and predictive models as well as with the analysis of generalized categorical variables.