Non-linear Multivariate Normalization Methods

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

Chapter Chapter 9 in Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems, 2023, pp 167-194 from Springer

Abstract: Abstract This chapter describes various functional transformations combined with a data normalization procedure in order to limit the influence of heterogeneities on the final ranking of alternatives in multi-criteria decision-making problems. The methods of non-linear data transformation are presented in two versions: pre-processing of initial data and post-processing of normalized values. Such a procedure can be caused by the presence of non-typical values in the data. The goal is to minimize the impact of atypical values on the rating of alternatives. The end result of successive transformations (both linear and non-linear) of the original data is their mapping onto the set [0, 1]. One of the transformation stages is the reduction of attributes to a dimensionless form based on linear normalization methods. A non-linear transformation allows you to redefine proportions (distances) between attribute values for different alternatives. Therefore, the entire chain of transformations can be defined as a non-linear normalization.

Keywords: Multivariate normalization; Non-linear methods; Asymmetry; Pre- and post-nonlinear processing of data (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-3-031-33837-3_9

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DOI: 10.1007/978-3-031-33837-3_9

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