Note: Intro -- Contents -- 1 Introduction -- 1.1 A Brief Literature Review -- 1.2 Outline of the Book -- References -- 2 A Brief Introduction to Fuzzy Sets -- 2.1 Basic Definitions and Properties of Fuzzy Sets -- 2.2 Basic Set-Theoretic Operations on Fuzzy Sets -- 2.3 Fuzzy Relations -- 2.4 Fuzzy Numbers and Fuzzy Arithmetic -- 2.5 Fuzzy Events and Their Probabilities -- 2.6 Defuzzification of Fuzzy Sets -- References -- 3 A Brief Introduction to Fuzzy Optimization and Fuzzy Mathematical Programming -- 3.1 Introductory Remarks -- 3.2 Main Approaches to Fuzzy Optimization -- 3.3 Bellman and Zadeh's General Approach to Decision Making Under Fuzziness -- 3.4 Using the α-cuts of the Fuzzy Feasible Set -- 3.5 Fuzzy Mathematical Programming -- 3.6 Fuzzy Linear Programming -- 3.7 Fuzzy Linear Programming with Fuzzy Constraints -- 3.8 Fuzzy Coefficients in the Objective Function -- 3.9 Fuzzy Coefficients in the Technological Matrix -- References -- 4 New Methods for Solving Fully Fuzzy Transportation Problems with Trapezoidal Fuzzy Parameters -- 4.1 Preliminaries -- 4.1.1 Basic Definitions Related to Fuzzy Numbers -- 4.1.2 Arithmetic Operations on the Trapezoid Fuzzy Numbers -- 4.2 A Fuzzy Linear Programming Formulation of the Balanced Fully Fuzzy Transportation Problem -- 4.3 Existing Methods for Finding a Fuzzy Optimal Solution of the Fully Fuzzy Transportation Problem -- 4.4 Liu and Kao's Method -- 4.4.1 Fully Fuzzy Transportation Problems with the Inequality Constraints -- 4.4.2 Fully Fuzzy Transportation Problems with Equality Constraints -- 4.5 A Critical Analysis of the Existing Methods -- 4.6 On Some New Methods for Solving the Fully Fuzzy Transportation Problem -- 4.6.1 A New Method Based on a Fuzzy Linear Programming Formulation -- 4.6.2 Method Based on the Tabular Representation -- 4.6.3 Advantages of the Proposed Methods over the Existing Methods. , 4.7 An Illustrative Example -- 4.7.1 Fuzzy Optimal Solution Using the Method Based on Fuzzy Linear Programming Formulation -- 4.7.2 Fuzzy Optimal Solution Using the Method Based on Tabular Representation -- 4.7.3 Interpretation of Results -- 4.8 Case Study -- 4.8.1 Description of the Problem -- 4.8.2 Results Obtained -- 4.8.3 Interpretation of Results -- 4.9 Concluding Remarks -- References -- 5 New Methods for Solving the Fully Fuzzy Transportation Problems with the LR Flat Fuzzy Numbers -- 5.1 Preliminaries -- 5.2 Basic Definitions -- 5.3 Arithmetic Operations on the LR Flat Fuzzy Numbers -- 5.4 Solution of the Fully Fuzzy Transportation Problems with Parameters Represented by the LR Fuzzy Numbers or LR Flat Fuzzy Numbers -- 5.5 New Methods -- 5.5.1 Method Based on Fuzzy Linear Programming -- 5.5.2 Method Based on the Tabular Representation -- 5.5.3 Main Advantages of the Proposed Methods -- 5.6 Illustrative Example -- 5.6.1 Determination of the Fuzzy Optimal Solution Using the Method Based on the Fuzzy Linear Programming -- 5.6.2 Determination of the Fuzzy Optimal Solution Using the Method Based on the Tabular Representation -- 5.6.3 Interpretation of Results -- 5.7 A Comparative Study -- 5.8 Concluding Remarks -- References -- 6 New Improved Methods for Solving the Fully Fuzzy Transshipment Problems with Parameters Given as the LR Flat Fuzzy Numbers -- 6.1 Fuzzy Linear Programming Formulation of the Balanced Fully Fuzzy Transshipment Problems -- 6.2 Outline of the Ghatee and Hashemi Method -- 6.3 On Some Limitations of the Existing Methods -- 6.4 New Methods -- 6.4.1 New Method Based on the Fuzzy Linear Programming Formulation -- 6.4.2 New Method Based on the Tabular Representation -- 6.4.3 Advantages of the New Methods -- 6.5 Illustrative Example. , 6.5.1 Determination of the Optimal Solution Using the Method Based on the Fuzzy Linear Programming Formulation -- 6.5.2 Determination of the Optimal Solution Using the Method Based on the Tabular Representation -- 6.5.3 Interpretation of Results -- 6.6 A Comparative Study -- 6.7 A Case Study -- 6.8 Concluding Remarks -- References -- 7 New Methods for Solving Fully Fuzzy Solid Transportation Problems with LR Fuzzy Parameters -- 7.1 Fuzzy Linear Programming Formulation of the Balanced Fully Fuzzy Solid Transportation Problems -- 7.2 Liu and Kao's Method -- 7.3 Some Shortcomings of Liu and Kao's Method -- 7.4 Limitations of the Methods Proposed in the Previous Chapters -- 7.5 New Methods -- 7.5.1 New Method Based on the Fuzzy Linear Programming Formulation -- 7.5.2 New Method Based on the Tabular Representation -- 7.5.3 Advantages of the New Methods -- 7.6 Illustrative Example -- 7.6.1 Determination of the Fuzzy Optimal Solution Using the New Method Based on the Fuzzy Linear Programming Formulation -- 7.6.2 Determination of the Fuzzy Optimal Solution Using the New Method Based on the Tabular Representation -- 7.6.3 Interpretation of Results -- 7.7 A Comparative Study -- 7.8 A Case Study -- 7.8.1 Problem Description -- 7.8.2 Results -- 7.8.3 Interpretation of Results -- 7.9 Concluding Remarks -- References -- 8 New Methods for Solving Fully Fuzzy Solid Transshipment Problems with LR Flat Fuzzy Numbers -- 8.1 New Fuzzy Linear Programming Formulation of the Balanced Fully Fuzzy Solid Transshipment Problem -- 8.2 Limitations of the Existing Method and Methods Proposed in Previous Chapters -- 8.3 New Methods -- 8.3.1 New Method Based on the Fuzzy Linear Programming Formulation -- 8.3.2 New Method Based on the Tabular Representation -- 8.3.3 Advantages of the New Methods -- 8.4 Illustrative Example. , 8.4.1 Determination of the Fuzzy Optimal Solution of the Fully Fuzzy Solid Transshipment Problem Using the Method Based on the Fuzzy Linear Programming Formulation -- 8.4.2 Determination of the Fuzzy Optimal Solution of the Fully Fuzzy Solid Transshipment Problem Using the Method Based on the Tabular Representation -- 8.4.3 Interpretation of Results -- 8.5 A Comparison of Results Obtained -- 8.6 Concluding Remarks -- References -- 9 Conclusions and Future Research Directions -- References.