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Full Description
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.
Contents
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.- 3.4. Conditions for Pareto Optimality in the Decision Space.- 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.- 4.3. Compromise Solutions.- 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.- 5.4. Further Comments.- Exercises.- 6. Some Basic Techniques for Constructing Value Functions.- 6.1. Constructing General Value Functions.- 6.2. Constructing Additive Value Functions.- 6.3. Approximation Method.- 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.- 7.4. 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.- 8.3. Generating the Set N from Nex-Points.- 8.4. MC2-Simplex Method and Potential Solutions in Linear Systems.- 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.- 9.3. Habitual Domains.- 9.4. Some Observations in Social Psychology.- 9.5. Some Applications.- 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.- 10.2. Preference over Uncertain Outcomes.- 10.3. Multicriteria Dynamic Optimization Problems.- 10.4. Second-Order Games.- Exercises.
