Ordinal scales in the theory of measurement
In the paper a new comparison criterion for a consistent assignment of real numbers to the elements of an empirical structure (usually called as scales in the theory of measurement) defined in sets ordered by a transitive, asymmetric binary relation is introduced, and complete characterisation of the structure of all equivalence classes of scales of such sets is given. Conditions for extendability of order-preserving functions defined on arbitrary subsets of the set \({\mathbb{R}}\) of real numbers with values in the same set to order-preserving functions defined on all of \({\mathbb{R}}\) are given.
extendability of order- preserving functions
scientific article; zbMATH DE number 3999732