CASE.EDU:    HOME | DIRECTORIES | SEARCH
case western reserve university

Behnam Malakooti, Ph.D., P.E.
 

Discrete Multiple Criteria Decision Making: Interactive and Ranking Methods

Behnam Malakooti

Brief Table Of Contents Detailed Table Of Contents

  • Part I. Convex, Tradeoff, Quasi-nondominancy, Utility Nondominancy, and Ranking with Partial Information

    • Chapter 1 Identifying Nondominated Alternatives with Partial Information
      Identifying Nondominated Alternatives with Partial Information for Multiple Objective Discrete and Linear Programming Problems (34)
      • 1. Introduction
      • 2. Convex and Utility Nondominancy; Reduction of Set of Discrete Alternatives
        • 2.1. Construction of Partial Information for Additive MAUFs
        • 2.2. Utility Nondominancy and Convex Nondominancy
      • 3. Trade-Off and Utility Nondominancy; Establishing the Most Preferred Alternative through Interactive Paired Comparison Methods
        • 3.1. Trade-Off Nondominancy and Utility Nondominancy
        • 3.2. Minimal Partial Information for Optimality
        • 3.3. An Interactive Paired Comparison Method
        • 3.4. Examples Demonstrating Concepts from Sections II and III
      • 4. Extensions to Multiple Objective Linear Programming Problems
        • 4.1. Converting Discrete MCDM Problems to MOLP Problems
        • 4.2. MOLP Problems and Efficiency (Nondominancy) Properties
        • 4.3. Utility Nondominancy for MOLP Problems
        • 4.4. Convergence Properties for Interactive Paired Comparison Methods for MOLP Problems
        • 4.5. Enumeration of All Utility Nondominated Alternatives for MOLP Problems
      • 5. Extensions to Quasi-Nondominancy and Reference Nondominancy
        • 5.1. Quasi-Nondominancy
        • 5.2. Reference Nondominancy
      • 6. Conclusion
      • 7. Appendix 1 (An Example of Utility Nondominancy for Alternatives and Trade-Offs)
      • 8. Utility Nondominated Alternatives
      • 9. Minimum Information for Optimality
      • 10. Appendix 2 (An Example for MOLP Problems)
      • 11. Appendix 3 (An Algorithm for Identifying Utility Nondominated Alternatives or Trade-Offs
        • 11.1. Identifying All Utility Nondominted Alternatives
        • 11.2. Identifying All Utility Nondominted and Nondominated Trade-Offs
        • 11.3. The Algorithm
      • 12. References

    • Part II. Strengths of Preferences and Imprecise Multi-Criteria Utility Functions

      • Chapter 2 Ranking Discrete Alternatives for Ordinal, Cardinal, and Strengths of Preferences: Efficient Algorithms
        • Ranking and Screening Multiple Criteria Alternatives with Partial Information and use of Ordinal and Cardinal Strength of Preferences (6)
        • 1. Abstract
        • 2. Introduction
        • 3. Some Theory and Ranking Algorithm for Screening and Ranking Alternatives with Partial Information
        • 4. Ranking Algorithm for Additive Multi-Attribute Utility Function
        • 5. Ordinal and Cardinal Strength of Preference, Generation of Partial Information, and Computational Experiments
        • 6. Conclusions
        • 7. References
      • Chapter 3 Ranking with Strengths of Preferences for Additive Utility Functions and Identifying Inconsistent Responses
        Assessment Through Strength of Preference (46)
        • 1. Introduction
        • 2. Elimination with Partial Information on Scaling Constants
        • 3. Rating Assessment with Strength of Preference
        • 4. An Interactive Paired Comparison Approach
        • 5. Inconsistency and a Resolution
        • 6. Elimination with Partial Information on Single Utility Functions
        • 7. Appendix A: An Example of Assessment Through Rating
        • 8. Appendix B: An Example of Assessment Through the Interactive Approach
        • 9. References
      • Chapter 4 Screening Discrete Alternatives with Imprecisely Assessed Additive Multiple Attribute Functions
        Screening Discrete Alternatives with Imprecisely Assessed Additive Multi-Attribute Functions (18)
        • 1. Abstract
        • 2. Statement of Scope and Purpose
        • 3. Introduction
        • 4. Basic Notations, Motivation, and Assessment of Partial Information
        • 5. Ranking with Partial Information on Scaling Constants: Utility Nondominancy
        • 6. Conclusions
        • 7. References
        • 8. Appendix A. An Example of the Utility Nondominancy Procedure for a Multilinear MAUF
        • 9. Appendix B. An Interactive Approach

    • Part III. Nonlinear Multiple Criteria Utility Functions

      • Chapter 5 Quasi-Convex and Quasi-Concave Multiple Criteria Utility Function Dominating Cones
        Ranking Multiple Criteria Alternatives with Half-Space, Convex, and Non-Convex Dominating Cones (32)
        • 1. Scope and Purpose
        • 2. Abstract
        • 3. Introduction
        • 4. A Quasi-Concave Multi-Attribute Utility Function
          • 4.1. Quasi-Concave MAUFs
          • 4.2. A Naïve Interactive Procedure
          • 4.3. An Example
          • 4.4. Relationship of Utility Functions, Quasi-Concavity. and Efficiency Definitions
        • 5. Ranking with Local Partial Information and Paired Comparison
          • 5.1. Partial Information on Weights
          • 5.2. An Example
          • 5.3. Paired Comparison Information to Rank Alternatives
          • 5.4. An Example
        • 6. Ranking with Non-Unique Weights at Given Alternatives
          • 6.1. Motivation and Definition
          • 6.2. An Example
          • 6.3. Ranking Alternatives with Partial Information on Weights (Non-Convex Cones)
          • 6.4. An Example
        • 7. Extensions for Quasi-Convex Multi-Attribute Utility Function
        • 8. Extensions of Previous Sections for Quasi-Convexity
        • 9. Some Procedures to Determine Whether MAUF is Quasi-Convex
        • 10. Conclusions
        • 11. References
      • Chapter 6 Quasi-Concave Utility: Exact Interactive Method
        Theories and an Exact Interactive Paired Comparison Approach for Discrete Multiple Criteria Problems (31)
        • 1. Introduction
        • 2. Use of Trade-Offs for Convergence and Elimination of Alternatives
          • 2.1. Definition of Trade-Offs
          • 2.2. Quasi-Concavity and Elimination of Utility Inefficient Alternatives
          • 2.3. Convex and Trade-Off Efficiency Definitions
          • 2.4. Convergence for Convex Points
          • 2.5. Identification of a Convex Efficient Subset for Convergence
          • 2.6. A Branching Procedure for Converting Nonconvex Cones to Convex Cones
        • 3. Use of Paired Comparisons for Ranking and Eliminating Alternatives
          • 3.1. Identification of Utility Efficient and Inefficient Alternatives
          • 3.2. Enlargement of the Cone Domain
          • 3.3. Use of Infeasible Points
          • 3.4. Testing Inconsistency of the DM
        • 4. An Interactive Method
          • 4.1. Use of Both Trade-Offs and Paired Comparisons to Eliminate Alternatives
          • 4.2. An Example of Generating Cones Using Trade-Offs and Paired Comparisons
          • 4.3. Generating Alternatives for the One-Dimension Search
          • 4.4. An Exact Interactive Algorithm
          • 4.5. Ranking and Inconsistency Check for Paired Comparison Information
          • 4.6. Converting Trade-Off Questions to Paired Comparison Questions
        • 5. Computational Experiments with the Method
          • 5.1. Effect of Paired Comparisons Instead of Trade-Offs
        • 6. Appendix 1. Two Examples
        • 7. References
      • Chapter 7 Quasi-Concave Utility: Heuristic, Two Point Cones, and Quick Ranking Methods
        A Decision Support System and a Heuristic Interactive Approach for Solving Discrete Multiple Criteria Problems (40)
        • 1. Introduction
        • 2. Two-Point Cones
          • 2.1. Clustering of Alternatives
          • 2.2. A Projection Approach for Finding Shadow Points
          • 2.3. A Procedure for Selecting Good Candidates
        • 3. Procedures for a Gradient-Based Approach
          • 3.1. Some Theory for the Approximation of the Gradient Through Paired Comparison Questions
          • 3.2. A Heuristic Method for Generating Local Adjacent Points
          • 3.3. A Procedure for Assisting Weights of Gradient by Strength of Preferences
          • 3.4. A Heuristic Method for Gradient Cuts
          • 3.5. A Heuristic Method for Generating Alternatives for the One-Dimensional Search
        • 4. A Gradient-Based Interactive Paired Comparison Approach
        • 5. Computational Experiments with the Method and Comparison to Other Methods
          • 5.1. Computational Experiences
          • 5.2. Comparison to Analytic Hierarchy Process
        • 6. A Decision Support System for Ranking Discrete Alternatives
          • 6.1. Quick Ranking by Lexicographic Ordering (Q-RALO)
          • 6.2. Quick Ranking by Identification of Trial Alternatives (Q-RITA)
          • 6.3. Quick Ranking by Assessment of Weights (Q-RAW)
          • 6.4. Ranking Alternatives with Strength of Preference (RASP)
          • 6.5. Gradient-Based Alternative Selection Procedure (GASP)
          • 6.6. Gradient-Based Unbound Search Technique (GUST)
        • 7. Conclusion
        • 8. Appendix (An Example)
        • 9. References
      • Chapter 8 Decision Support System Multiple Criteria Decision Making and Hierarchical Methods
        A Decision Support System and a Heuristic Interactive Approach for Solving Discrete Multiple Criteria Problems (40)
        • 1. Introduction
        • 2. Two-Point Cones
          • 2.1. Clustering of Alternatives
          • 2.2. A Projection Approach for Finding Shadow Points
          • 2.3. A Procedure for Selecting Good Candidates
        • 3. Procedures for a Gradient-Based Approach
          • 3.1. Some Theory for the Approximation of the Gradient Through Paired Comparison Questions
          • 3.2. A Heuristic Method for Generating Local Adjacent Points
          • 3.3. A Procedure for Assisting Weights of Gradient by Strength of Preferences
          • 3.4. A Heuristic Method for Gradient Cuts
          • 3.5. A Heuristic Method for Generating Alternatives for the One-Dimensional Search
        • 4. A Gradient-Based Interactive Paired Comparison Approach
        • 5. Computational Experiments with the Method and Comparison to Other Methods
          • 5.1. Computational Experiences
          • 5.2. Comparison to Analytic Hierarchy Process
        • 6. A Decision Support System for Ranking Discrete Alternatives
          • 6.1. Quick Ranking by Lexicographic Ordering (Q-RALO)
          • 6.2. Quick Ranking by Identification of Trial Alternatives (Q-RITA)
          • 6.3. Quick Ranking by Assessment of Weights (Q-RAW)
          • 6.4. Ranking Alternatives with Strength of Preference (RASP)
          • 6.5. Gradient-Based Alternative Selection Procedure (GASP)
          • 6.6. Gradient-Based Unbound Search Technique (GUST)
        • 7. Conclusion
        • 8. Appendix (An Example)
        • 9. References
      • Chapter 9 Decision Support System Multiple Criteria Decision Making: Certainty, Uncertainty, and Hierarchical
        A Decision Support System for Discrete Multi-Criteria Problems: Under Certainty, Uncertainty, and Hierarchical (22)
        • 1. Abstract
        • 2. Introduction
        • 3. Data Entry, Assessment, and Summary
          • 3.1. Assessment of Single-Attribute Value Functions by the DM
          • 3.2. Statistics and Matrix of Extreme Values
        • 4. Screening Methods
          • 4.1. Efficiency (Nondominancy)
          • 4.2. Reference Efficiency (Reference Nondominancy)
          • 4.3. Convex Efficiency
          • 4.4. Bounds on Criteria (Objective) Values
          • 4.5. Bounds on Criteria (Objective) Weights
          • 4.6. Ranking of Objective Weights
        • 5. Complete Ranking Methods
          • 5.1. Simple Utility Function Forms for Trial and Error Approach
          • 5.2. Assessment of Additive Utility Functions
          • 5.3. Concave and Convex Quadratic Utility Functions
          • 5.4. Artificial Neural Network Utility Functions
          • 5.5. Consistency and Sensitivity Analysis
        • 6. Finding the Best Alternative (Interactive Methods)
          • 6.1. Quasi-Concave Utility Functions: A Gradient-Based Alternative Selection Procedure
          • 6.2. Quasi-Convex Utility Functions
          • 6.3. Unknown Nonlinear Utility Functions: A Gradient-Based Unbounded Search Technique
        • 7. Extension to Problems under Uncertainty
        • 8. Solving Discrete Pay-Off Matrix (One Criterion)
        • 9. Solving Discrete MCDM Problems Under Uncertainty
        • 10. Hierarchical and Large-Scale Multi-Criteria Problems
        • 11. Results of Some Experiments and a Guide to use the Package
          • 11.1. Experimental Results and Discussions
          • 11.2. A Guide to Choose Appropriate Methods
        • 12. Conclusions
        • 13. References
      • Chapter 10 Machine Set-Up Applications with Interactive Quasi-Concave Utility Functions
        An Interactive Multiple Criteria Approach for Parameter Selection in Metal Cutting (36)
        • 1. Introduction
        • 2. Mathematical Formulation of the Machining Operation
          • 2.1. Nomenclature
          • 2.2. Decision Variables (Parameters to be Assessed)
          • 2.3. Objective Function
          • 2.4. Problem Constraints
        • 3. An Interactive Heuristic Gradient-Based Multicriteria Approach
          • 3.1. Discrete Multiple Criteria Problem
          • 3.2. Assessment of the Gradient
          • 3.3. A Heuristic Gradient Cut
          • 3.4. One-Dimensional Search
          • 3.5. An Interactive Method
        • 4. Multiple Criteria Decision Making Method for Machining Operation
          • 4.1. Discrete Variable Approach for Generating Efficient Alternatives
          • 4.2. Interactive Discrete MCDM Approach for Machining Operations
        • 5. Example
        • 6. Computational Experiments and Comparison to Commercial Packages
          • 6.1. Experiments with the Example Problem for Interval m and Objective Bounds
          • 6.2. Experiments of Five Problems
          • 6.3. Comparison to Commercial Packages
        • 7. Decision Support Systems for Machining Operations
        • 8. Conclusions
        • 9. Acknowledgements
        • 10. References
        • 11. Contributors