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Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems
Inversion, Displacement, Asymmetry
Buch von Irik Z. Mukhametzyanov
Sprache: Englisch

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Beschreibung
This book presents a systematic review of multidimensional normalization methods and addresses problems frequently encountered when using various methods and ways to eliminate them.

The invariant properties of the linear normalization methods presented here can be used to eliminate simple problems and avoid obvious errors when choosing a normalization method. The book introduces valuable, novel techniques for the multistep normalization of multidimensional data. One of these methods involves inverting the normalized values of cost attributes into profit attributes based on the reverse sorting algorithm (ReS algorithm). Another approach presented is the IZ method, which addresses the issue of shift in normalized attribute values. Additionally, a new method for normalizing the decision matrix is proposed, called the MS method, which ensures the equalization of average values and variances of attributes.

Featuring numerous illustrative examples throughout, the book helps readers to understand what difficulties can arise in multidimensional normalization, what to expect from such problems, and how to solve them. It is intended for academics and professionals in various areas of data science, computing in mathematics, and statistics, as well as decision-making and operations.
This book presents a systematic review of multidimensional normalization methods and addresses problems frequently encountered when using various methods and ways to eliminate them.

The invariant properties of the linear normalization methods presented here can be used to eliminate simple problems and avoid obvious errors when choosing a normalization method. The book introduces valuable, novel techniques for the multistep normalization of multidimensional data. One of these methods involves inverting the normalized values of cost attributes into profit attributes based on the reverse sorting algorithm (ReS algorithm). Another approach presented is the IZ method, which addresses the issue of shift in normalized attribute values. Additionally, a new method for normalizing the decision matrix is proposed, called the MS method, which ensures the equalization of average values and variances of attributes.

Featuring numerous illustrative examples throughout, the book helps readers to understand what difficulties can arise in multidimensional normalization, what to expect from such problems, and how to solve them. It is intended for academics and professionals in various areas of data science, computing in mathematics, and statistics, as well as decision-making and operations.
Über den Autor

Irik Z. Mukhametzyanov is a Professor at Higher School of Information and Social Technology, department of Information Technologies and Applied Mathematics, Ufa State Petroleum Technological University (USPTU), Russia. His current research interests include multivariate analysis, mathematical modeling and optimization in socio-economic systems, design and analysis of multi-agent systems, fuzzy systems, decision support systems, and multi-criteria decision-making models.

Zusammenfassung

Provides a systematic review of multidimensional normalization methods

Includes multi-step normalization to manage data inversion method

Introduces domain displacement of normalized values and data asymmetry methods

Inhaltsverzeichnis
Introduction.- The MCDM Rank Model.- Normalization and rank model MCDM.- Linear Methods for Multivariate Normalization.- Inversion of normalized values. ReS-algorithm.- Rank Reversal in MCDM Models. Contribution of the normalization.- Coordination of scales of normalized values. IZ-method MS-transformation of Z-Score.- Nonlinear multivariate normalization methods.- Normalization for the case "Nominal value the best".- Comparative results of ranking of alternatives using different normalization methods. Computational experiment.- 12 Significant difference of the performance indicator of alternatives.- Conclusion
Details
Erscheinungsjahr: 2023
Fachbereich: Allgemeines
Genre: Wirtschaft
Rubrik: Recht & Wirtschaft
Medium: Buch
Reihe: International Series in Operations Research & Management Science
Inhalt: xxix
292 S.
2 s/w Illustr.
93 farbige Illustr.
292 p. 95 illus.
93 illus. in color.
ISBN-13: 9783031338366
ISBN-10: 3031338367
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Mukhametzyanov, Irik Z.
Hersteller: Springer International Publishing
Springer International Publishing AG
International Series in Operations Research & Management Science
Maße: 241 x 160 x 24 mm
Von/Mit: Irik Z. Mukhametzyanov
Erscheinungsdatum: 26.07.2023
Gewicht: 0,653 kg
Artikel-ID: 126864869
Über den Autor

Irik Z. Mukhametzyanov is a Professor at Higher School of Information and Social Technology, department of Information Technologies and Applied Mathematics, Ufa State Petroleum Technological University (USPTU), Russia. His current research interests include multivariate analysis, mathematical modeling and optimization in socio-economic systems, design and analysis of multi-agent systems, fuzzy systems, decision support systems, and multi-criteria decision-making models.

Zusammenfassung

Provides a systematic review of multidimensional normalization methods

Includes multi-step normalization to manage data inversion method

Introduces domain displacement of normalized values and data asymmetry methods

Inhaltsverzeichnis
Introduction.- The MCDM Rank Model.- Normalization and rank model MCDM.- Linear Methods for Multivariate Normalization.- Inversion of normalized values. ReS-algorithm.- Rank Reversal in MCDM Models. Contribution of the normalization.- Coordination of scales of normalized values. IZ-method MS-transformation of Z-Score.- Nonlinear multivariate normalization methods.- Normalization for the case "Nominal value the best".- Comparative results of ranking of alternatives using different normalization methods. Computational experiment.- 12 Significant difference of the performance indicator of alternatives.- Conclusion
Details
Erscheinungsjahr: 2023
Fachbereich: Allgemeines
Genre: Wirtschaft
Rubrik: Recht & Wirtschaft
Medium: Buch
Reihe: International Series in Operations Research & Management Science
Inhalt: xxix
292 S.
2 s/w Illustr.
93 farbige Illustr.
292 p. 95 illus.
93 illus. in color.
ISBN-13: 9783031338366
ISBN-10: 3031338367
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Mukhametzyanov, Irik Z.
Hersteller: Springer International Publishing
Springer International Publishing AG
International Series in Operations Research & Management Science
Maße: 241 x 160 x 24 mm
Von/Mit: Irik Z. Mukhametzyanov
Erscheinungsdatum: 26.07.2023
Gewicht: 0,653 kg
Artikel-ID: 126864869
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