OMID BOZORG-HADDAD, PhD, is Professor in the Department of Irrigation & Reclamation Engineering at University of Tehran, Iran.BABAK ZOLGHADR-ASLI, M.Sc., received the M.Sc. in Irrigation Engineering, Water Resources Management, from Tehran University, Iran. HUGO A. LOÁICIGA, PhD, is Professor of Geography in the Department of Geography at the University of California, Santa Barbara, USA.

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• Preface xiii1 An Overview of the Art of Decision-making 11.1 Introduction 11.2 Classification of MADM Methods 51.2.1 Preference Evaluation Mechanism 51.2.2 Attributes’ Interactions 71.2.3 The Mathematical Nature of Attributes’ Values 81.2.3.1 Deterministic Vs. Nondeterministic 81.2.3.2 Fuzzy Vs. Crisp 81.2.4 Number of Involved Decision-makers 81.3 Brief Chronicle of MADM Methods 91.4 Conclusion 10References 122 Simple Weighting Methods: Weighted Sum and Weighted Product Methods 172.1 Introduction 172.2 The Weighted Sum Method 202.2.1 Step 1: Defining the Decision-making Problem 202.2.2 Step 2: Normalizing the Elements of the Decision-matrix 212.2.3 Step 3: Aggregating the Preference of Alternatives 212.3 The Weighted Product Method 212.4 Conclusion 22References 223 Analytic Hierarchy Process (AHP) 253.1 Introduction 253.2 The Hierarchical Structure 273.3 The Pairwise Comparison 303.4 Inconsistency 333.5 Quadruple Axioms of the AHP 353.6 Stepwise Description of the AHP Method 363.6.1 Step 1: Defining the Decision-making Problem 363.6.2 Step 2: Performing the Pairwise Comparison Through the Hierarchical Structure 373.6.3 Step 3: Estimating the Preference Value Vectors 373.6.4 Step 4: Synthesizing and Computing the Overall Preference Value of Alternatives 383.6.5 Step 5: Evaluating the Results’ Rationality and Selecting the Best Alternative 383.7 Conclusion 39References 394 Analytic Network Process (ANP) 434.1 Introduction 434.2 Network Vs. Hierarchy Structure 454.3 Stepwise Instruction to the ANP Method 484.3.1 Step 1: Defining the Decision-making Problem 484.3.2 Step 2: Conducting a Pairwise Comparison of the Elements of the  Decision-making Problem 494.3.3 Step 3: Forming the Supermatrix 524.3.4 Step 4: Computing the Weighted Supermatrix 534.3.5 Step 5: Computing the Global Priority Vectors and Choosing the Most Suitable Alternative 534.4 Conclusion 54References 545 The Best–Worst Method (BWM) 595.1 Introduction 595.2 Basic Principles of the BWM 625.3 Stepwise Description of the BWM 635.3.1 Step 1: Defining the Decision-Making Problem 645.3.2 Step 2: Determining the Reference Criteria 645.3.3 Step 3: Pairwise Comparisons 645.3.4 Step 4: Computing the Optimal Weights 655.3.5 Step 5: Measuring the Inconsistency of Decision-Makers Judgments 665.4 Conclusion 67References 676 TOPSIS 716.1 Introduction 716.2 Stepwise Description of the TOPSIS Method 726.2.1 Step 1: Establishing the Formation of the Decision-making Problem 736.2.2 Step 2: Normalizing the Element of the Decision-matrix 736.2.3 Step 3: Computing theWeighted Normalized Preference Values 746.2.4 Step 4: Defining the Reference Alternatives 746.2.5 Step 5: Calculation of the Separation Measure 756.2.6 Step 6: Computing the Relative Closeness to the Ideal Solution 766.2.7 Step 7: Ranking the Alternatives 766.3 A Common Misinterpretation of TOPSIS Results 766.4 Conclusion 77References 787 VIKOR 817.1 Introduction 817.2 Stepwise Description of the VIKOR Method 847.2.1 Step 1: Modeling the Decision-Making Problem 847.2.2 Step 2: Normalizing the Element of the Decision-Matrix 857.2.3 Step 3: Compute the “Group Satisfaction” and “Individual Regret” Parameters 857.2.4 Step 4: Computing the VIKOR Parameter 867.2.5 Step 5: Ranking the Alternatives 867.2.6 Step 6: Determining the Compromise Solution 867.3 Conclusion 87References 888 ELECTRE 918.1 Introduction 918.2 A Brief History of the ELECTRE Family of Methods 938.3 ELECTRE I 948.4 ELECTRE II 968.5 ELECTRE III 998.6 ELECTRE IV 1048.7 Conclusion 105References 1069 PROMETHEE 1119.1 Introduction 1119.2 Common Ground of the PROMETHEE Family 1129.2.1 Stage 1: Construction of the Generalized Criteria 1139.2.2 Stage 2: Mapping the Outrank Relation on the Set of Feasible Alternatives 1169.2.3 Stage 3: Evaluation the Relation Among the Feasible Alternatives 1169.3 PROMETHEE I 1179.4 PROMETHEE II 1189.5 PROMETHEE III 1199.6 PROMETHEE IV 1209.7 Conclusion 121References 12110 Superiority and Inferiority Ranking (SIR) 12510.1 Introduction 12510.2 Foundational Bases of the SIR Method 12610.3 Stepwise Description of the SIR Method 12910.3.1 Step 1: Establishing the Formation of the Decision-Making Problem 12910.3.2 Step 2: Computing the Superiority and Inferiority Scores 12910.3.3 Step 3: Forming the Superiority and Inferiority Matrices 13210.3.4 Step 4: Superiority and Inferiority Flows 13310.3.5 Step 5: Ranking the Set of Feasible Alternatives 13510.4 Conclusion 136References 13711 PAPRIKA 13911.1 Introduction 13911.2 Stepwise Description of PAPRIKA 14011.2.1 Step 1: Defining the Decision-Making Problem 14111.2.2 Step 2: Identifying the Nondominated Pairs of Alternative 14111.2.3 Step 3: Ranking the Pairs of Nondominated Solutions 14211.2.4 Step 4: Calculating the Complete Ranking of Alternatives 14411.3 Conclusion 145References 14612 Gray Relational Analysis 14912.1 Introduction 14912.2 Gray System Theory: The Foundation and Basic Principles 15012.3 Gray Relational Modeling 15112.4 Gray Theory in Relation to MADM 15312.5 Conclusion 155References 155A Weight Assignment Approaches 159A.1 Subjective Approach: Weighted Least Squares 160A.2 Objective Approach: Multiobjective Programming Model 162References 164B A Benchmark Example and a Comparison between Objective- and Subjective-Based MADM Methods 167References 171Index 173

OMID BOZORG-HADDAD, PhD, is Professor in the Department of Irrigation & Reclamation Engineering at University of Tehran, Iran.BABAK ZOLGHADR-ASLI, M.Sc., received the M.Sc. in Irrigation Engineering, Water Resources Management, from Tehran University, Iran. HUGO A. LOÁICIGA, PhD, is Professor of Geography in the Department of Geography at the University of California, Santa Barbara, USA.

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• Preface xiii1 An Overview of the Art of Decision-making 11.1 Introduction 11.2 Classification of MADM Methods 51.2.1 Preference Evaluation Mechanism 51.2.2 Attributes’ Interactions 71.2.3 The Mathematical Nature of Attributes’ Values 81.2.3.1 Deterministic Vs. Nondeterministic 81.2.3.2 Fuzzy Vs. Crisp 81.2.4 Number of Involved Decision-makers 81.3 Brief Chronicle of MADM Methods 91.4 Conclusion 10References 122 Simple Weighting Methods: Weighted Sum and Weighted Product Methods 172.1 Introduction 172.2 The Weighted Sum Method 202.2.1 Step 1: Defining the Decision-making Problem 202.2.2 Step 2: Normalizing the Elements of the Decision-matrix 212.2.3 Step 3: Aggregating the Preference of Alternatives 212.3 The Weighted Product Method 212.4 Conclusion 22References 223 Analytic Hierarchy Process (AHP) 253.1 Introduction 253.2 The Hierarchical Structure 273.3 The Pairwise Comparison 303.4 Inconsistency 333.5 Quadruple Axioms of the AHP 353.6 Stepwise Description of the AHP Method 363.6.1 Step 1: Defining the Decision-making Problem 363.6.2 Step 2: Performing the Pairwise Comparison Through the Hierarchical Structure 373.6.3 Step 3: Estimating the Preference Value Vectors 373.6.4 Step 4: Synthesizing and Computing the Overall Preference Value of Alternatives 383.6.5 Step 5: Evaluating the Results’ Rationality and Selecting the Best Alternative 383.7 Conclusion 39References 394 Analytic Network Process (ANP) 434.1 Introduction 434.2 Network Vs. Hierarchy Structure 454.3 Stepwise Instruction to the ANP Method 484.3.1 Step 1: Defining the Decision-making Problem 484.3.2 Step 2: Conducting a Pairwise Comparison of the Elements of the  Decision-making Problem 494.3.3 Step 3: Forming the Supermatrix 524.3.4 Step 4: Computing the Weighted Supermatrix 534.3.5 Step 5: Computing the Global Priority Vectors and Choosing the Most Suitable Alternative 534.4 Conclusion 54References 545 The Best–Worst Method (BWM) 595.1 Introduction 595.2 Basic Principles of the BWM 625.3 Stepwise Description of the BWM 635.3.1 Step 1: Defining the Decision-Making Problem 645.3.2 Step 2: Determining the Reference Criteria 645.3.3 Step 3: Pairwise Comparisons 645.3.4 Step 4: Computing the Optimal Weights 655.3.5 Step 5: Measuring the Inconsistency of Decision-Makers Judgments 665.4 Conclusion 67References 676 TOPSIS 716.1 Introduction 716.2 Stepwise Description of the TOPSIS Method 726.2.1 Step 1: Establishing the Formation of the Decision-making Problem 736.2.2 Step 2: Normalizing the Element of the Decision-matrix 736.2.3 Step 3: Computing theWeighted Normalized Preference Values 746.2.4 Step 4: Defining the Reference Alternatives 746.2.5 Step 5: Calculation of the Separation Measure 756.2.6 Step 6: Computing the Relative Closeness to the Ideal Solution 766.2.7 Step 7: Ranking the Alternatives 766.3 A Common Misinterpretation of TOPSIS Results 766.4 Conclusion 77References 787 VIKOR 817.1 Introduction 817.2 Stepwise Description of the VIKOR Method 847.2.1 Step 1: Modeling the Decision-Making Problem 847.2.2 Step 2: Normalizing the Element of the Decision-Matrix 857.2.3 Step 3: Compute the “Group Satisfaction” and “Individual Regret” Parameters 857.2.4 Step 4: Computing the VIKOR Parameter 867.2.5 Step 5: Ranking the Alternatives 867.2.6 Step 6: Determining the Compromise Solution 867.3 Conclusion 87References 888 ELECTRE 918.1 Introduction 918.2 A Brief History of the ELECTRE Family of Methods 938.3 ELECTRE I 948.4 ELECTRE II 968.5 ELECTRE III 998.6 ELECTRE IV 1048.7 Conclusion 105References 1069 PROMETHEE 1119.1 Introduction 1119.2 Common Ground of the PROMETHEE Family 1129.2.1 Stage 1: Construction of the Generalized Criteria 1139.2.2 Stage 2: Mapping the Outrank Relation on the Set of Feasible Alternatives 1169.2.3 Stage 3: Evaluation the Relation Among the Feasible Alternatives 1169.3 PROMETHEE I 1179.4 PROMETHEE II 1189.5 PROMETHEE III 1199.6 PROMETHEE IV 1209.7 Conclusion 121References 12110 Superiority and Inferiority Ranking (SIR) 12510.1 Introduction 12510.2 Foundational Bases of the SIR Method 12610.3 Stepwise Description of the SIR Method 12910.3.1 Step 1: Establishing the Formation of the Decision-Making Problem 12910.3.2 Step 2: Computing the Superiority and Inferiority Scores 12910.3.3 Step 3: Forming the Superiority and Inferiority Matrices 13210.3.4 Step 4: Superiority and Inferiority Flows 13310.3.5 Step 5: Ranking the Set of Feasible Alternatives 13510.4 Conclusion 136References 13711 PAPRIKA 13911.1 Introduction 13911.2 Stepwise Description of PAPRIKA 14011.2.1 Step 1: Defining the Decision-Making Problem 14111.2.2 Step 2: Identifying the Nondominated Pairs of Alternative 14111.2.3 Step 3: Ranking the Pairs of Nondominated Solutions 14211.2.4 Step 4: Calculating the Complete Ranking of Alternatives 14411.3 Conclusion 145References 14612 Gray Relational Analysis 14912.1 Introduction 14912.2 Gray System Theory: The Foundation and Basic Principles 15012.3 Gray Relational Modeling 15112.4 Gray Theory in Relation to MADM 15312.5 Conclusion 155References 155A Weight Assignment Approaches 159A.1 Subjective Approach: Weighted Least Squares 160A.2 Objective Approach: Multiobjective Programming Model 162References 164B A Benchmark Example and a Comparison between Objective- and Subjective-Based MADM Methods 167References 171Index 173

OMID BOZORG-HADDAD, PhD, is Professor in the Department of Irrigation & Reclamation Engineering at University of Tehran, Iran.BABAK ZOLGHADR-ASLI, M.Sc., received the M.Sc. in Irrigation Engineering, Water Resources Management, from Tehran University, Iran. HUGO A. LOÁICIGA, PhD, is Professor of Geography in the Department of Geography at the University of California, Santa Barbara, USA.

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• Preface xiii1 An Overview of the Art of Decision-making 11.1 Introduction 11.2 Classification of MADM Methods 51.2.1 Preference Evaluation Mechanism 51.2.2 Attributes’ Interactions 71.2.3 The Mathematical Nature of Attributes’ Values 81.2.3.1 Deterministic Vs. Nondeterministic 81.2.3.2 Fuzzy Vs. Crisp 81.2.4 Number of Involved Decision-makers 81.3 Brief Chronicle of MADM Methods 91.4 Conclusion 10References 122 Simple Weighting Methods: Weighted Sum and Weighted Product Methods 172.1 Introduction 172.2 The Weighted Sum Method 202.2.1 Step 1: Defining the Decision-making Problem 202.2.2 Step 2: Normalizing the Elements of the Decision-matrix 212.2.3 Step 3: Aggregating the Preference of Alternatives 212.3 The Weighted Product Method 212.4 Conclusion 22References 223 Analytic Hierarchy Process (AHP) 253.1 Introduction 253.2 The Hierarchical Structure 273.3 The Pairwise Comparison 303.4 Inconsistency 333.5 Quadruple Axioms of the AHP 353.6 Stepwise Description of the AHP Method 363.6.1 Step 1: Defining the Decision-making Problem 363.6.2 Step 2: Performing the Pairwise Comparison Through the Hierarchical Structure 373.6.3 Step 3: Estimating the Preference Value Vectors 373.6.4 Step 4: Synthesizing and Computing the Overall Preference Value of Alternatives 383.6.5 Step 5: Evaluating the Results’ Rationality and Selecting the Best Alternative 383.7 Conclusion 39References 394 Analytic Network Process (ANP) 434.1 Introduction 434.2 Network Vs. Hierarchy Structure 454.3 Stepwise Instruction to the ANP Method 484.3.1 Step 1: Defining the Decision-making Problem 484.3.2 Step 2: Conducting a Pairwise Comparison of the Elements of the  Decision-making Problem 494.3.3 Step 3: Forming the Supermatrix 524.3.4 Step 4: Computing the Weighted Supermatrix 534.3.5 Step 5: Computing the Global Priority Vectors and Choosing the Most Suitable Alternative 534.4 Conclusion 54References 545 The Best–Worst Method (BWM) 595.1 Introduction 595.2 Basic Principles of the BWM 625.3 Stepwise Description of the BWM 635.3.1 Step 1: Defining the Decision-Making Problem 645.3.2 Step 2: Determining the Reference Criteria 645.3.3 Step 3: Pairwise Comparisons 645.3.4 Step 4: Computing the Optimal Weights 655.3.5 Step 5: Measuring the Inconsistency of Decision-Makers Judgments 665.4 Conclusion 67References 676 TOPSIS 716.1 Introduction 716.2 Stepwise Description of the TOPSIS Method 726.2.1 Step 1: Establishing the Formation of the Decision-making Problem 736.2.2 Step 2: Normalizing the Element of the Decision-matrix 736.2.3 Step 3: Computing theWeighted Normalized Preference Values 746.2.4 Step 4: Defining the Reference Alternatives 746.2.5 Step 5: Calculation of the Separation Measure 756.2.6 Step 6: Computing the Relative Closeness to the Ideal Solution 766.2.7 Step 7: Ranking the Alternatives 766.3 A Common Misinterpretation of TOPSIS Results 766.4 Conclusion 77References 787 VIKOR 817.1 Introduction 817.2 Stepwise Description of the VIKOR Method 847.2.1 Step 1: Modeling the Decision-Making Problem 847.2.2 Step 2: Normalizing the Element of the Decision-Matrix 857.2.3 Step 3: Compute the “Group Satisfaction” and “Individual Regret” Parameters 857.2.4 Step 4: Computing the VIKOR Parameter 867.2.5 Step 5: Ranking the Alternatives 867.2.6 Step 6: Determining the Compromise Solution 867.3 Conclusion 87References 888 ELECTRE 918.1 Introduction 918.2 A Brief History of the ELECTRE Family of Methods 938.3 ELECTRE I 948.4 ELECTRE II 968.5 ELECTRE III 998.6 ELECTRE IV 1048.7 Conclusion 105References 1069 PROMETHEE 1119.1 Introduction 1119.2 Common Ground of the PROMETHEE Family 1129.2.1 Stage 1: Construction of the Generalized Criteria 1139.2.2 Stage 2: Mapping the Outrank Relation on the Set of Feasible Alternatives 1169.2.3 Stage 3: Evaluation the Relation Among the Feasible Alternatives 1169.3 PROMETHEE I 1179.4 PROMETHEE II 1189.5 PROMETHEE III 1199.6 PROMETHEE IV 1209.7 Conclusion 121References 12110 Superiority and Inferiority Ranking (SIR) 12510.1 Introduction 12510.2 Foundational Bases of the SIR Method 12610.3 Stepwise Description of the SIR Method 12910.3.1 Step 1: Establishing the Formation of the Decision-Making Problem 12910.3.2 Step 2: Computing the Superiority and Inferiority Scores 12910.3.3 Step 3: Forming the Superiority and Inferiority Matrices 13210.3.4 Step 4: Superiority and Inferiority Flows 13310.3.5 Step 5: Ranking the Set of Feasible Alternatives 13510.4 Conclusion 136References 13711 PAPRIKA 13911.1 Introduction 13911.2 Stepwise Description of PAPRIKA 14011.2.1 Step 1: Defining the Decision-Making Problem 14111.2.2 Step 2: Identifying the Nondominated Pairs of Alternative 14111.2.3 Step 3: Ranking the Pairs of Nondominated Solutions 14211.2.4 Step 4: Calculating the Complete Ranking of Alternatives 14411.3 Conclusion 145References 14612 Gray Relational Analysis 14912.1 Introduction 14912.2 Gray System Theory: The Foundation and Basic Principles 15012.3 Gray Relational Modeling 15112.4 Gray Theory in Relation to MADM 15312.5 Conclusion 155References 155A Weight Assignment Approaches 159A.1 Subjective Approach: Weighted Least Squares 160A.2 Objective Approach: Multiobjective Programming Model 162References 164B A Benchmark Example and a Comparison between Objective- and Subjective-Based MADM Methods 167References 171Index 173