Basic Principles and Techniques of Normalization of Multidimensional Data
DOI:
https://doi.org/10.2298/YJOR250115004MKeywords:
Normalization of multivariate data, MCDM, scale coordination, linear transformations of normalized values, data normalization principles, the rank reversal phenomenonAbstract
The paper presents the main approaches and methods of multivariate data normalization in the context of MCDM problems. A technique for normalizing multivariate data is presented that results in: 1) equal "upper" bound of the value’s interval for all attributes (Up.Norm); 2) equal "upper" and "lower" bounds (IZ.Norm); 3) equal "mean" values (Mean.Norm); 4) equal "mean" and "upper" (or "lower") bound (Dist.Norm); 5) equal "mean" and "range" (MS.Norm). The entire pool of solutions is aimed at preventing the hidden priority of the contribution of individual attributes to the integral indicator that determines the ranking of alternatives. The interpretation of normalized values for different methods made it possible to expand the range of methods based on the arithmetic mean and to identify normalization methods based on harmonic, geometric, counterharmonic, quadratic, and median means. A generalization of the methodology for nonlinear normalization of multivariate data is presented, along with an algorithm for normalizing target criteria consistent with linear normalization methods. Numerical experiments demonstrate the existence of MCDC problems that are highly sensitive to the choice of normalization method, which creates not only uncertainty but also the impossibility of multicriteria selection using ranking methods.
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