Logical methods for studying relations in criterial spaces with arbitrary ordinal scales

Proposed was an approach enabling one to reduce studies of the properties of ordinal relations for criteria with an arbitrary (including finite) set of values to similar problems for relations defined over the entire $n$-dimensional real space $\mathbf R^n$. It enabled one to prove that all main findings, methods, and algorithms obtained previously for the ordinal relations on $\mathbf R^n$ can be extended in arbitrary criterial spaces to the ordinal relations with the criterion scale cardinalities not less than three.