Multi-Criteria and Multi-Dimensional Analysis in Decisions: Decision Making with Preference Vector Methods (PVM) and Vector Measure Construction Methods (VMCM) (Vector Optimization)

✍ Scribed by Kesra Nermend

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 366
• Category: Library

✦ Synopsis

A new era is emerging in which a group of quantitative methods featuring characteristics of multidimensional comparative analysis (MCA) and multi-criteria decision-making analysis (MCDA) can be used to automate objective decision-making processes. This book introduces the character of the criteria (desirable, non-desirable, motivating, demotivating, and neutral) to MCDA and MCA methods. It presents the author’s own developed methods, the preference vector method (PVM), for solving multi-criteria problems in decision making; and, vector measure construction method (VMCM), which is dedicated to solving typical problems in the field of multidimensional comparative analysis. All methods are explained step by step with relevant examples, primarily in the fields of economics and management.

✦ Table of Contents

Preface
List of Major Markings
General Markings
TOPSIS
VIKOR
ELECTRE
PROMETHEE
AHP,ANP
REMBRANDT
DEMATEL
PVM
Contents
1 The Issue of Multi-criteria and Multi-dimensionality in Decision Support
1.1 Decision-Making Process
1.2 Review of Decision Support Methods
Part I Multidimensional Comparative Analysis Methods
2 Initial Procedure for Data Analysis
2.1 Selection and Definition of the Character of Variables
2.2 Determination of Weights of Variables
2.3 Normalization of Variables
2.3.1 Studies on Ai Properties
2.3.2 Studies on Bi Properties
3 Methods of Building the Aggregate Measures
3.1 Patternless Reference Methods
3.2 Distance Reference Pattern-Based Methods
3.3 Vector Reference Methods
3.4 Theoretical Basis of the VMCM Method
3.5 Description of Vector Measure Construction Method (VMCM)
3.5.1 Stage 1: Selection of Variables
3.5.2 Stage 2: Elimination of Variables
3.5.3 Stage 3: Defining the Diagnostic Variables Character
3.5.4 Stage 4: Assigning Weights to Diagnostic Variables
3.5.5 Stage 5: Normalization of Variables
3.5.6 Stage 6: Determination of Pattern and Anti-pattern
3.5.7 Stage 7: Construction of the Synthetic Measure
3.5.8 Stage 8: Classification of Objects
3.6 Grouping Objects Based on the Aggregate Measure Value
Part II Multi-criteria Decision Support Methods
4 Methods Based on an Outranking Relationship
4.1 The Concept of Preference Relations in Multi-Criteria Methods
4.2 ELECTRE Methods
4.3 PROMETHEE Method
5 Methods Based on Utility Function
5.1 Analytical Hierarchy Process AHP
5.2 The Analytical Network Process ANP
5.2.1 Calculating AHP Using ANP
5.2.2 An Example of Using the ANP Method to Select an IT System
5.3 REMBRANDT Method
5.4 DEMATEL Method
6 Multi-criteria Methods Using the Reference Points Approach
6.1 TOPSIS Multi-criteria Method
6.2 VIKOR Multi-criteria Method
6.3 Examples of Calculating Aggregate Measures
6.4 Multi-criteria Preference Vector Method (PVM)
6.4.1 Description of the Preference Vector Method (PVM)
6.4.2 Stages I and II: Formulation of Decision Problem and Defining Decision Variants
6.4.2.1 III. Setting Evaluation Criteria for Decision Variants
6.4.2.2 IV. Defining the Criteria Character
6.4.2.3 Stage V. Attributing Weights to the Criteria
6.4.2.4 Stage VI. Normalizing the Criteria
6.4.2.5 Stage VII. Determining the Preference Vector
6.4.2.6 Stage VIII. Determination of Importance Factor
6.4.2.7 Stage IX. Ranking of Variants
6.4.2.8 Stage X. Calculation of the Importance Factor Including Subjective Criteria
6.4.3 PVM Method Calculation Example
6.5 Comparison of the PVM Method with Selected Multi-criteria Methods
6.6 PVM Method in Decision-Making Support
6.6.1 Preference Vector Method in Decision-Making Support
6.6.2 Variant 1. Assessment of European Countries in Terms of the Quality of Life of Their Residents
6.6.3 Variant 2. Assessment of Education Disparities in European Countries
6.6.4 Variant 3. Assessment of EU Countries' Friendliness Toward Business Start-Ups
6.6.5 Variant 4. Assessment of the Labor Market Situation
6.6.6 Variant 5. Assessment of Countries in Terms of Housing Conditions for Retired Persons
6.6.7 Variant 6. Assessment of Living Standards of EUResidents
6.6.8 Application of the PVM Method in Consumer Decision Support
Conclusion
Bibliography
Index