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Table of Contents
Intro
Preface
Contents
About the Author
List of Abbreviations
List of Figures
List of Tables
Chapter 1: Introduction
1.1 The Problem of Multi-criteria Decision-Making
1.2 Multidimensional Normalization in the Context of Decision Problems
References
Chapter 2: The MCDM Rank Model
2.1 MCDM Rank Model
2.2 The Target Value of Attributes
2.3 Significance of Criteria: Multivariate Assessment
2.3.1 Subjective Weighting Methods: Pairwise Comparisons and AHP Process
2.3.2 Subjective Weighting Methods: Best-Worst Method
2.3.3 Objective Weighting Methods: Entropy, CRITIC, SD
Entropy Weighting Method (EWM) [26, 27, 37]
CRiteria Importance Through Inter-criteria Correlation (CRITIC) [28]
Standard Deviation (SD)
2.4 Aggregation of the Attributes: An Overview of Some Methods
2.4.1 Value Measurement Methods
Simple Additive Weighting (SAW) or Weighted Sum Method (WSM) [1]
Weighted Product Method (WPM) [39]
Weighted Aggregated Sum Product Assessment (WASPAS) [39]
Multi-Attributive Border Approximation Area Comparison (MABAC) [45]
Complex Proportional Assessment (COPRAS) Method [46]
2.4.2 Goal or Reference Level Models
Distance Metric
Reference Point (RP) Method [47]
COmbinative Distance-based ASsessment (CODAS)
Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [1]
VIsekriterijumsko KOmpromisno Rangiranje (VIKOR) [40]
Gray Relation Analysis (GRA) [49, 50]
2.4.3 Outranking Techniques
Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) [41]
Organisazion, RangEment ot SynTEze de donnecs relationnelles (ORESTE) [43, 44]
2.4.4 Rank Reversal Problem
2.4.5 Distinguishability of the Performance Indicator of Alternatives
2.5 Design of the MCDM Model
2.6 Conclusions
References
Chapter 3: Normalization and MCDM Rank Model
3.1 General Principles for Normalizing Multidimensional Data
3.1.1 Preserving the Ordering Values of Attributes
3.1.2 Scale Invariance of Normalized Values of Attributes
3.1.3 Principle of Additive Significance of Attributes
3.1.4 Interpretation of Normalized Values of Attributes
3.2 Linear Multivariate Normalization Methods
3.2.1 How Is the Shift Factor Determined?
3.2.2 How Is Scaling Determined?
3.2.3 Disadvantages of Data Standardization
3.3 Asymmetry in the Distribution of Features
3.3.1 Measures of Asymmetry
3.4 The Outlier Detection
3.5 Non-linear Normalization: General Principles
3.6 Target Inversion in Multivariate Normalization
3.7 Isotropy of Scales of Normalized Values
3.8 Impact of the Choice of Normalization Method on the Rating
3.9 Conclusions
References
Chapter 4: Linear Methods for Multivariate Normalization
4.1 Basic Linear Methods for Multivariate Normalization
4.2 Scaling Factor Ratios
Preface
Contents
About the Author
List of Abbreviations
List of Figures
List of Tables
Chapter 1: Introduction
1.1 The Problem of Multi-criteria Decision-Making
1.2 Multidimensional Normalization in the Context of Decision Problems
References
Chapter 2: The MCDM Rank Model
2.1 MCDM Rank Model
2.2 The Target Value of Attributes
2.3 Significance of Criteria: Multivariate Assessment
2.3.1 Subjective Weighting Methods: Pairwise Comparisons and AHP Process
2.3.2 Subjective Weighting Methods: Best-Worst Method
2.3.3 Objective Weighting Methods: Entropy, CRITIC, SD
Entropy Weighting Method (EWM) [26, 27, 37]
CRiteria Importance Through Inter-criteria Correlation (CRITIC) [28]
Standard Deviation (SD)
2.4 Aggregation of the Attributes: An Overview of Some Methods
2.4.1 Value Measurement Methods
Simple Additive Weighting (SAW) or Weighted Sum Method (WSM) [1]
Weighted Product Method (WPM) [39]
Weighted Aggregated Sum Product Assessment (WASPAS) [39]
Multi-Attributive Border Approximation Area Comparison (MABAC) [45]
Complex Proportional Assessment (COPRAS) Method [46]
2.4.2 Goal or Reference Level Models
Distance Metric
Reference Point (RP) Method [47]
COmbinative Distance-based ASsessment (CODAS)
Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [1]
VIsekriterijumsko KOmpromisno Rangiranje (VIKOR) [40]
Gray Relation Analysis (GRA) [49, 50]
2.4.3 Outranking Techniques
Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) [41]
Organisazion, RangEment ot SynTEze de donnecs relationnelles (ORESTE) [43, 44]
2.4.4 Rank Reversal Problem
2.4.5 Distinguishability of the Performance Indicator of Alternatives
2.5 Design of the MCDM Model
2.6 Conclusions
References
Chapter 3: Normalization and MCDM Rank Model
3.1 General Principles for Normalizing Multidimensional Data
3.1.1 Preserving the Ordering Values of Attributes
3.1.2 Scale Invariance of Normalized Values of Attributes
3.1.3 Principle of Additive Significance of Attributes
3.1.4 Interpretation of Normalized Values of Attributes
3.2 Linear Multivariate Normalization Methods
3.2.1 How Is the Shift Factor Determined?
3.2.2 How Is Scaling Determined?
3.2.3 Disadvantages of Data Standardization
3.3 Asymmetry in the Distribution of Features
3.3.1 Measures of Asymmetry
3.4 The Outlier Detection
3.5 Non-linear Normalization: General Principles
3.6 Target Inversion in Multivariate Normalization
3.7 Isotropy of Scales of Normalized Values
3.8 Impact of the Choice of Normalization Method on the Rating
3.9 Conclusions
References
Chapter 4: Linear Methods for Multivariate Normalization
4.1 Basic Linear Methods for Multivariate Normalization
4.2 Scaling Factor Ratios