Multiple-Criteria Decision Making

1. Introduction.- 1.1. The Needs and Basic Elements.- 1.2. An Overview of the Book.- 1.3. Notation.- 2. Binary Relations.- 2.1. Preference as a Binary Relation.- 2.2. Characteristics of Preferences.- 2.3. Optimality Condition.- 2.4. Further Comments.- Exercises.- 3. Pareto Optimal or Efficient Solutions.- 3.1. Introduction.- 3.2. General Properties of Pareto Optimal Solutions.- 3.3. Conditions for Pareto Optimality in the Outcome Space.- 3.3.1. Conditions for a General Y.- 3.3.2. Conditions when Y Is ??-Convex.- 3.3.3. Boundedness of Tradeoff and Proper Efficiency.- 3.4. Conditions for Pareto Optimality in the Decision Space.- 3.4.1. Conditions in Terms of Single Criterion Maximization.- 3.4.2. Conditions in Terms of Differentiability.- 3.4.3. Decomposition Theorems of X0(??) and X0(?>).- 3.4.4. An Example.- 3.5. Further Comments.- 3.6. Appendix: Generalized Gordon Theorem.- 3.7. Appendix: Optimality Conditions.- Exercises.- 4. Goal Setting and Compromise Solutions.- 4.1. Introduction.- 4.2. Satisficing Solutions.- 4.2.1. Goal Setting.- 4.2.2. Preference Ordering and Optimality in Satisficing Solutions.- 4.2.3. Mathematical Programs and Interactive Methods.- 4.3. Compromise Solutions.- 4.3.1. Basic Concepts.- 4.3.2. General Properties of Compromise Solutions.- 4.3.3. Properties Related to p.- 4.3.4. Computing Compromise Solutions.- 4.3.5. Interactive Methods.- 4.4. Further Comments.- Exercises.- 5. Value Function.- 5.1. Revealed Preference from a Value Function.- 5.2. Conditions for Value Functions to Exist.- 5.3. Additive and Monotonic Value Functions and Preference Separability.- 5.3.1. Additive and Monotonic Value Functions and Implied Preference Separability.- 5.3.2. Conditions for Additive and Monotonic Value Functions.- 5.3.3. Structures of Preference Separability and Value Functions.- 5.4. Further Comments.- Exercises.- 6. Some Basic Techniques for Constructing Value Functions.- 6.1. Constructing General Value Functions.- 6.1.1. Constructing Indifference Curves (Surfaces).- 6.1.2. Constructing the Tangent Planes and the Gradients of Value Functions.- 6.1.3. Constructing the Value Function.- 6.2. Constructing Additive Value Functions.- 6.2.1. A First Method for Constructing Additive Value Functions.- 6.2.2. A Second Method for Constructing Additive Value Functions.- 6.3. Approximation Method.- 6.3.1. A General Concept.- 6.3.2. Approximation for Additive Value Functions.- 6.3.3. Eigenweight Vectors for Additive Value Functions.- 6.3.4. Least-Distance Approximation Methods.- 6.4. Further Comments.- 6.5. Appendix: Perron-Frobenius Theorem.- Exercises.- 7. Domination Structures and Nondominated Solutions.- 7.1. Introduction.- 7.2. Domination Structures.- 7.3. Constant Dominated Cone Structures.- 7.3.1. Cones and their Polars.- 7.3.2. General Properties of N-Points.- 7.3.3. A Characterization of N-Points.- 7.3.4. Cone-Convexity and N-Points.- 7.3.5. N-Points in the Decision Space.- 7.3.6. Existence, Properness, and Duality Questions.- 7.4. Local and Global N-Points in Domination Structures.- 7.5. Interactive Approximations for N-Points with Information from Domination Structures.- 7.6. Further Comments.- 7.7. Appendix: A Constructive Proof of Theorem 7.3.- Exercises.- 8. Linear Cases, MC- and MC2-Simplex Methods.- 8.1. N-Points in the Linear Case.- 8.2. MC-Simplex Method and Nex-Points.- 8.2.1. MC-Simplex Method and Set of Optimal Weights.- 8.2.2. Decomposition of the Weight Space.- 8.2.3. Connectedness and Adjacency of Nex-Points, and a Method for Locating Nex Set.- 8.3. Generating the Set N from Nex-Points.- 8.3.1. The Need for the Entire Set N.- 8.3.2. Decomposition of the Set N into Nondominated Faces.- 8.3.3. Method to Locate All N-Faces and Examples.- 8.4. MC2-Simplex Method and Potential Solutions in Linear Systems.- 8.4.1. Introduction.- 8.4.2. Potential Solutions of Linear Systems.- 8.4.3. The MC2-Simplex Method.- 8.4.4. Separation, Adjacency, and Connectedness.- 8.4.5. Duality of MC2 Programs.- 8.4.6. An Example.- 8.5. Further Comments.- 8.6. Appendix: Proof of Lemma 8.2.- Exercises.- 9. Behavioral Bases and Habitual Domains of Decision Making.- 9.1. Introduction.- 9.2. Behavioral Bases for Decision Making.- 9.2.1. A Model for Decision/Behavior Processes-Overview.- 9.2.2. Internal Information Processing Center-The Brain.- 9.2.3. Goal Setting, Self-Suggestion, and State Valuation.- 9.2.4. Charge Structures and Significance Ordering of Events.- 9.2.5. Least Resistance Principle, Discharge, and Problem Solving.- 9.2.6. External Information Inputs.- 9.3. Habitual Domains.- 9.3.1. Definition and Formation of Stable Habitual Domains.- 9.3.2. The Expansion of Habitual Domains.- 9.3.3. Interaction of Different Habitual Domains.- 9.3.4. Implications of Studying Habitual Domains.- 9.4. Some Observations in Social Psychology.- 9.4.1. Social Comparison Theory.- 9.4.2. Halo Effect.- 9.4.3. Projection Effect (Assumed Similarity).- 9.4.4. Proximity Theory.- 9.4.5. Reciprocation Behaviors.- 9.4.6. Similarity Effect.- 9.4.7. Scapegoating Behavior (Displacement of Aggression).- 9.4.8. Responsibility Diffusion or Deindividuation in Group Behavior.- 9.5. Some Applications.- 9.5.1. Self-Awareness, Happiness, and Success.- 9.5.2. Decision Making.- 9.5.3. Persuasion, Negotiation, and Gaming.- 9.5.4. Career Management.- 9.6. Further Comments.- 9.7. Appendix: Existence of Stable Habitual Domains.- Exercises.- 10. Further Topics.- 10.1. Interactive Methods for Maximizing Preference Value Functions.- 10.1.1. Adapted Gradient Search Method.- 10.1.2. Surrogate Worth Tradeoff Method.- 10.1.3. Zionts-Wallenius Method.- 10.2. Preference over Uncertain Outcomes.- 10.2.1. Stochastic Dominance (Concepts Based on CDF).- 10.2.2. Mean-Variance Dominance (Concepts Based on Moments).- 10.2.3. Probability Dominance (Concept Based on Outperforming Probability).- 10.2.4. Utility Dominance (Concept Based on Utility Functions).- 10.2.5. Some Interesting Results.- 10.3. Multicriteria Dynamic Optimization Problems.- 10.3.1. Finite Stage Dynamic Programs with Multicriteria.- 10.3.2. Optimal Control with Multicriteria.- 10.4. Second-Order Games.- 10.4.1. Decision Elements and Decision Dynamics.- 10.4.2. Second-Order Games.- 10.4.3. Second-Order Games and Habitual Domains.- Exercises.