Elimination of the Domains’ Displacement of the Normalized Values in MCDM Tasks: The IZ-Method

Abstract

Decision matrix normalization is an important step in ranking-based MCDM methods. Different normalization methods can produce different final rankings. The paper provides an overview and defines the invariant properties of the basic linear methods of multidimensional normalization. It is shown that one of the essential reasons for the variation of the ranking depending on the normalization method is the domains’ displacement of the normalized values of various attributes relative to each other. An IZ-method for multidimensional normalization is proposed, which eliminates the domains’ displacement. The IZ-method ensures the preservation of dispositions of natural values of attribute, provides symmetry in an orientation toward optimizing costs and benefits, processes the zero and negative values, and eliminates the priority of the contributions of various criteria to the performance indicator of alternatives. The IZ-method converts multivariate data to a single common scale and represents a class of multivariate normalization methods that convert data to isotropic scales. The IZ-method allows binding to the scale of any feature or to the scale chosen by the decision maker. Efficiency of the IZ-method is postulated by the totality of the fulfillment of the basic principles and required properties for multidimensional normalization.