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Non-linear Multivariate Normalization Methods

In: Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems

Author

Listed:
  • Irik Z. Mukhametzyanov

    (Ufa State Petroleum Technological University)

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.

Suggested Citation

  • Irik Z. Mukhametzyanov, 2023. "Non-linear Multivariate Normalization Methods," International Series in Operations Research & Management Science, in: Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems, chapter 0, pages 167-194, Springer.
    • Handle: RePEc:spr:isochp:978-3-031-33837-3_9
    DOI: 10.1007/978-3-031-33837-3_9
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