Multiple-Criteria Decision Making

This book is an outgrowth of formal graduate courses in multiple-criteria decision making (MCDM) that the author has taught at the University of Rochester, University of Texas at Austin, and University of Kansas since 1972. The purpose is, on one hand, to offer the reader an integral and systematic view of various concepts and techniques in MCDM at an "introductory" level, and, on the other hand, to provide a basic conception of the human decision mechanism, which may improve our ability to apply the techniques we have learned and may broaden our llJ.ind for modeling human decision making. The book is written with a goal in mind that the reader should be able to assimilate and benefit from most of the concepts in the book if he has the mathematical maturity equivalent to a course in operations research or optimiz­ ation theory. Good training in linear and nonlinear programming is sufficient to digest, perhaps easily, most of the concepts in the book.

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.