Rating the diversity in sets of objects by referring to transformations as criteria

summary – The starting point of this study is the definition of two concepts expressing how a set of transformations acting within a domain may represent an upper or a lower bound of the diversity existing in any subset of that domain. The subject of analysis is then gradually expanded, by considering partitions (rather than subsets) of the domain, families of sets of transformations (rather than just one such set), and sets of objects indirectly related to the domain (rather than sets directly included in it). The main concepts defined in this study are explored in their formal properties and illustrated by examples. The introductory and concluding sections include comments on the motivation for the study and the possible merits of the method discussed.