SOME ASPECTS OF QUALITATIVE DATA-ANALYSIS

Let n greater-than-or-equal-to 1 be an arbitrary natural number and le t X, X1,..., X(n) be arbitrary (qualitative) random variables. Then it is the main aim of this paper to study and to characterize real-value d functions S(X) or S(X, X1,..., X(n)) which are comparable with the d egree up to which the variables X, X1,..., X(n) are known. Functions S (X) appear for example as expectations or as goodness criteria for a h omogeneity or heterogeneity function X in cluster analysis, while func tions S(X, X1) may appear as similarity or dissimilarity coefficients (correlation coefficients) or as stress measures in multi-dimensional scaling (MDS) if X and X, represent similarity or dissimilarity coeffi cients. In addition, if X1,..., X(n) are observed random variables, th en S(X, X1,..., X(n)) may be an objective function which has to be opt imized in order to estimate the unknown variable X.