Preference relations with interval estimation of replacements in a criterial space

The axioms are described in the binary preference relation with interval estimation of replacements in the criterial space and this relation is shown to be dictated by a multihedral cone of a special shape. The concept of replacement coefficients is extended to the case of an arbitrary binary preference relation in a criterial space; the properties are studied of extended coefficients for a relation with an interval estimation of replacements. Ways are considered of designing the multihedral cone on the knowledge of constraints imposed on conventional replacement coefficients and of replacement coefficient variables.