Fuzzy Multiple Objective Decision Making

In the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, control theory, artificial intelligence/expert system, etc. In this volume, methods and applications of crisp, fuzzy and possibilistic multiple objective decision making are first systematically and thoroughly reviewed and classified. This state-of-the-art survey provides readers with a capsule look into the existing methods, and their characteristics and applicability to analysis of fuzzy and possibilistic programming problems. To realize practical fuzzy modelling, it presents solutions for real-world problems including production/manufacturing, location, logistics, environment management, banking/finance, personnel, marketing, accounting, agriculture economics and data analysis. This book is a guided tour through the literature in the rapidly growing fields of operations research and decision making and includes the most up-to-date bibliographical listing of literature on the topic.

1 Introduction.- 1.1 Objectives of This Study.- 1.2 (Fuzzy) Multiple Objective Decision Making.- 1.3 Classification of (Fuzzy) Multiple Objective Decision Making.- 1.4 Applications of (Fuzzy) Multiple Objective Decision Making.- 1.5 Literature Survey.- 1.6 Fuzzy Sets.- 2 Multiple Objective Decision Making.- 2.1 Introduction.- 2.2 Goal Programming.- 2.2a A Portfolio Selection Problem.- 2.2b An Audit Sampling Problem.- 2.3 Fuzzy Programming.- 2.3.1 Max-Min Approach.- 2.3.1a A Trade Balance Problem.- 2.3.1b A Media Selection Problem.- 2.3.2 Augmented Max-Min Approach.- Example.- 2.3.2a A Trade Balance Problem.- 2.3.2b A Logistics Planning Model.- 2.3.3 Parametric Approach.- Example.- 2.4 Global Criterion Approach.- 2.4.1 Global Criterion Approach.- 2.4.1a A Nutrition Problem.- 2.4.2 TOPSIS for MODM.- 2. .2a A Water Quality Management Problem.- 2.5 Interactive Multiple Objective Decision Making.- 2.5.1 Optimal System Design.- 2.5.1a A Production Planning Problem.- 2.5.2 KSU-STEM.- 2.5.2a A Nutrition Problem.- 2.5.2b A Project Scheduling Problem.- 2.5.3 ISGP-II.- 2.5.3a A Nutrition Problem.- 2.5.3b A Bank Balance Sheet Management Problem.- 2.5.4 Augmented Min-Max Approach.- 2.5.4a A Water Pollution Control Problem.- 2.6 Multiple Objective Linear Fractional Programming.- 2.6.1 Luhandjula’s Approach.- Example.- 2.6.2 Lee and Tcha’s Approach.- 2.6.2a A Financial Structure Optimization Problem.- 2.7 Multiple Objective Geometric Programming.- Example.- 2.7a A Postal Regulation Problem.- 3 Fuzzy Multiple Objective Decision Making.- 3.1 Fuzzy Goal Programming.- 3.1.1 Fuzzy Goal Programming.- 3.1.1a A Production-Marketing Problem.- 3.1.1b An Optimal Control Problem.- 3.1.1c A Facility Location Problem.- 3.1.2 Preemptive Fuzzy Goal Programming.- Example: The Production-Marketing Problem.- 3.1.3 Interpolated Membership Function.- 3.1.3.1 Hannan’s Method.- Example: The Production-Marketing Problem.- 3.1.3.2 Inuiguchi, Ichihashi and Kume’s Method.- Example: The Trade Balance Problem.- 3.1.3.3 Yang, Ignizio and Kim’s Method.- Example.- 3.1.4 Weighted Additive Model.- 3.1.4.1 Crisp Weights.- 3.1.4.1a Maximin Approach.- Example: The Production-Marketing Problem.- 3.1.4.1b Augmented Maximin Approach.- 3.1.4.1c Supertransitive Approximation.- Example: The Production-Marketing Problem.- 3.1.4.2 Fuzzy Weights.- Example: The Production-Marketing Problem.- 3.1.5 A Preference Structure on Aspiration Levels.- Example: The Production-Marketing Problem.- 3.1.6 Nested Priority.- 3.1.6a A Personnel Selection Problem.- 3.2 Fuzzy Global Criterion.- Example.- 3.3 Interactive Fuzzy Multiple Objective Decision Making.- 3.3.1 Werners’s Method.- Example: The Trade Balance Problem.- 3.3.1a An Aggregate Production Planning Problem.- 3.3.2 Lai and Hwang’s Method.- 3.3.3 Leung’s Method.- Example.- 3.3.4 Fabian, Ciobanu and Stoica’s Method.- Example.- 3.3.5 Sasaki, Nakahara, Gen and Ida’s Method.- Example.- 3.3.6 Baptistella and Ollero’s Method.- 3.3.6a An Optimal Scheduling Problem.- 4 Possibilistic Multiple Objective Decision Making.- 4.1 Introduction.- 4.1.1 Resolution of Imprecise Objective Functions.- 4.1.2 Resolution of Imprecise Constraints.- 4.2 Possibilistic Multiple Objective Decision Making.- 4.2.1 Tanaka and His Col1eragues’ Methods.- Example.- 4.2.1.1 Possibilistic Regression.- Example 1.- Example 2.- 4.2.1.2 Possibilistic Group Method of Data Handling.- Example 28.- 4.2.2 Lai and Hwang’s Method.- 4.2.3 Negi’s Method.- Example.- 4.2.4 Luhandjula’s Method.- Example.- 4.2.5 Li and Lee’s Method.- Example.- 4.2.6 Wierzchon’s Method.- 4.3 Interactive Methods for PMODM.- 4.3.1 Sakawa and Yano’s Method.- Example.- 4.3.2 Slowinski’s Method.- 4.3.2a A Long-Term Development Planning Problem of a Water Supply System.- 4.3.2b A Land-Use Planning Problem.- 4.3.2c A Farm Structure Optimization Problem.- 4.3.3 Rommelranger’s Method.- Example.- 4.4 Hybrid Problems.- 4.4.1 Tanaka, Ichihashi and Asai’s Method.- Example.- 4.4.2 Inuiguchi and Ichihashi’s Method.- Example.- 4.5 Possibilistic Multiple Objective Linear Fractional Programming.- 4.6 Interactive Possibilistic Regression.- 4.6.1 Crisp Output and Crisp Input.- Example.- 4.6.2 Imprecise Output and Crisp Input.- Example.- 4.6.3 Imprecise Output and Imprecise Input.- Example.- 5 Concluding Remarks.- 5.1 Future Research.- 5.2 Fuzzy Mathematical Programming.- 5.3 Multiple Attribute Decision Making.- 5.4 Fuzzy Multiple Attribute Decision Making.- 5.5 Group Decision Making under Multiple Criteria.- Books, Monographs and Conference Proceedings.- Journal Articles, Technical Reports and Theses.- Appendix: Stochastic Programming.- A.1 Stochastic Programming with a Single Objective Function.- A.1.1 Distribution Problems.- A.1.2 Two-Stage Programming.- A.1.3 Chance-Constrained Programming.- A.2 Stochastic Programming with Multiple Objective Functions.- A.2.1 Distribution Problem.- A.2.2 Goal Programming Problem.- A.2.3 Utility Function Problem.- A.2.4 Interactive Problem.- References.