Coordination of Scales of Normalized Values: IZ-Method

Irik Z. Mukhametzyanov
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Irik Z. Mukhametzyanov: Ufa State Petroleum Technological University

Chapter Chapter 7 in Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems, 2023, pp 129-149 from Springer

Abstract: Abstract Despite applying the same transformation, the values of each feature are transformed independently during multivariate normalization. In particular, for linear normalization methods for each feature, the compression and shift coefficients are individual and are determined by a set of feature values of different alternatives, “measured” in the scale of this feature. As a result, it is possible to shift the area of normalized values of various features relative to each other and different data compression. This entails the priority of the contribution of individual criteria in the performance indicator of alternatives and is one of the significant reasons for the variation in the ranking results depending on the normalization method. To eliminate differences in the contributions of individual attributes to the performance indicator of alternatives by shifting the domains of normalized values, it is proposed to transform the area of normalized values. This transformation was performed on the basis of the IZ-method proposed by the author. The IZ-method converts multidimensional data to a single common scale and represents a class of multivariate normalization methods that convert to isotropic scales.

Keywords: Multivariate normalization; Domains displacement; Elimination of displacement; Conditionally general scale; IZ-method; IZ transformation for non-linear aggregation methods (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/978-3-031-33837-3_7

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