The axiomatic approach to introducing measures for ordering and classification of descriptive sets

In this work, a system of axioms of similarity measures for two descriptive sets is given. These sets include two groups: the axioms containing only information about two comparable objects and those relating to a family of the descriptive sets, in general. The axioms of relative similarity and inclusion measures are presented. The notion of equivalence between similarity measures was introduced. On its basis, several classes of equivalent similarity measures were established. We consider the conformity of similarity measures and data ordering algorithms. Some examples of measures used in biology are given.