MS-Transformation of Z-Score

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

Chapter Chapter 8 in Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems, 2023, pp 151-166 from Springer

Abstract: Abstract The attraction of Z-standardization for solving MCDM problems is that in this case, the domains of normalized values are aligned on average and the interpretation of the scales of normalized values is the same. The numerical values of all attributes are measured in the standard deviation scale of each feature. This has the advantage that such normalized values differ only in properties other than variability, facilitating, for example, shape comparisons. MS-transformations of standardized values to the set [0, 1] are proposed, for which the mean values and variances are the same for all attributes, and the domains of normalized values are averaged out. Additionally, the choice of the measurement scale is set in accordance with the selected normalization method. The exclusion of negative Z-scores allows you to expand the list of methods in decision-making for the transformed data. For example, it becomes valid to use WPM, WASPAS methods. The MS-method is relevant for non-linear aggregation methods and provides the choice of a conditionally general normalization scale that has the same interpretation of the normalized values as the main linear normalization methods. MS-transformation is applicable to data transformation of any centered value, and such an implementation is made for the mIQR normalization method, which expands the list of normalization methods with an adequate interpretation of normalized scales.

Keywords: Multivariate normalization; Data centered; MS-transformations of centered data; MS-transformations for nonlinear aggregation methods (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/978-3-031-33837-3_8

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