Note: Intro -- Preface -- Acknowledgements -- Contents -- 1 Matrix Games with Interval Payoffs -- 1.1 Matrix Games with Interval Payoffs -- 1.2 Existing Mathematical Formulation of Matrix Games with Interval Payoffs -- 1.3 Literature Review of Matrix Game with Interval Payoffs -- 1.4 Arithmetic Operations over Intervals -- 1.5 Flaws of the Existing Methods -- 1.6 Invalidity of Existing Mathematical Formulation of Matrix Games with Interval Payoffs -- 1.6.1 Existing Method to Obtain Mathematical Formulation of Matrix Games with Interval Payoffs -- 1.6.2 Mathematically Incorrect Assumptions Considered in the Existing Method -- 1.7 Minimum and Maximum of Intervals -- 1.7.1 Minimum of Intervals -- 1.7.2 Maximum of Intervals -- 1.8 Proposed Gaurika Method -- 1.8.1 Minimum Expected Gain of Player I -- 1.8.2 Maximum Expected Loss of Player II -- 1.9 Numerical Examples -- 1.9.1 Existing Numerical Example Considered by Nayak and Pal -- 1.9.2 Existing Numerical Example Considered by Li et al. -- 1.10 Conclusion -- References -- 2 Matrix Games with Fuzzy Payoffs -- 2.1 Matrix Games with Fuzzy Payoffs -- 2.2 Preliminaries -- 2.2.1 Some Basic Definitions -- 2.2.2 Arithmetic Operations of Trapezoidal Fuzzy Numbers -- 2.2.3 Comparison of Fuzzy Numbers -- 2.3 Existing Mathematical Formulation of Matrix Games with Fuzzy Payoffs -- 2.4 Literature Review of Matrix Games with Fuzzy Payoffs -- 2.5 Flaws of the Existing Methods -- 2.6 Invalidity of Existing Mathematical Formulation of Matrix Games with Fuzzy Payoffs -- 2.7 Proposed Mehar Method -- 2.7.1 Minimum Expected Gain of Player I -- 2.7.2 Maximum Expected Loss of Player II -- 2.8 Numerical Example -- 2.8.1 Minimum Expected Gain of Player I -- 2.8.2 Maximum Expected Loss of Player II -- 2.9 Conclusion -- References -- 3 Constrained Matrix Games with Fuzzy Payoffs -- 3.1 Constrained Matrix Games with Fuzzy Payoffs. , 3.2 Existing Mathematical Formulation of Constrained Matrix Games with Fuzzy Payoffs -- 3.3 Literature Review of Constrained Matrix Games with Fuzzy Payoffs -- 3.4 Flaws of the Existing Methods -- 3.5 Proposed Vaishnavi Method -- 3.5.1 Minimum Expected Gain of Player I -- 3.5.2 Maximum Expected Loss of Player II -- 3.6 Numerical Examples -- 3.6.1 Existing Numerical Example Considered by Li and Hong -- 3.6.2 Existing Numerical Example Considered by Li and Cheng -- 3.7 Conclusion -- References -- 4 Matrix Games with Intuitionistic Fuzzy Payoffs -- 4.1 Matrix Games with Intuitionistic Fuzzy Payoffs -- 4.2 Preliminaries -- 4.2.1 Basic Definitions -- 4.2.2 Arithmetic Operations over Trapezoidal Vague Sets -- 4.3 Existing Mathematical Formulation of Matrix Games with Intuitionistic Fuzzy Payoffs -- 4.4 Literature Review of Matrix Games with Intuitionistic Fuzzy Payoffs -- 4.5 Flaws of the Existing Methods -- 4.6 Proposed Ambika Methods -- 4.6.1 Ambika Method-I -- 4.6.2 Ambika Method-II -- 4.6.3 Ambika Method-III -- 4.6.4 Ambika Method-IV -- 4.7 Numerical Examples -- 4.7.1 Existing Numerical Example Considered by Nan et al. -- 4.7.2 Existing Numerical Example Considered by Li et al. -- 4.7.3 Existing Numerical Example Considered by Nan et al. -- 4.7.4 Existing Numerical Example Considered by Nan et al. -- 4.8 Conclusion -- References -- 5 Bimatrix Games with Intuitionistic Fuzzy Payoffs -- 5.1 The Difference-Index Based Ranking Method -- 5.2 Maximum of Trapezoidal Intuitionistic Fuzzy Numbers -- 5.3 Flaws in the Existing Mathematical Formulation of Bimatrix Games with Intuitionistic Fuzzy Payoffs -- 5.3.1 Mathematical Formulation of Bimatrix Games with Intuitionistic Fuzzy Payoffs -- 5.3.2 Mathematically Incorrect Assumption Considered by Li and Yang -- 5.4 Exact Solution of Bimatrix Games with Intuitionistic Fuzzy Payoffs. , 5.4.1 Exact Mathematical Formulation of Bimatrix Games with Intuitionistic Fuzzy Payoffs -- 5.4.2 Proposed Mehar Method -- 5.4.3 Convergence of the Proposed Mehar Method -- 5.5 Numerical Example -- 5.6 Conclusion -- References -- 6 Future Scope -- References.

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.

Note: Intro -- Preface -- Contents -- Abstract -- 1 State of the Art -- References -- 2 Non-negative Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constraints -- 2.1 Preliminaries -- 2.1.1 Basic Definitions -- 2.1.2 Arithmetic Operations -- 2.2 Existing Method for Solving Fully Fuzzy Linear -- 2.3 Limitations and Shortcoming of the Existing Method -- 2.3.1 Limitations of the Existing Method -- 2.3.2 Shortcoming of the Existing Method -- 2.4 Product of a Non-negative Trapezoidal Fuzzy Number with Unrestricted Trapezoidal Fuzzy Number -- 2.5 Kumar et al.'s Method to Find the Non-negative Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constraints -- 2.6 Illustrative Examples -- 2.6.1 Fuzzy Optimal Solution of the Chosen Fully Fuzzy Linear Programming Problems -- 2.7 Advantages of the Kumar et al.'s Method -- 2.8 Comparative Study -- 2.9 Conclusions -- References -- 3 Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constrains -- 3.1 Limitations of the Previous Presented Method -- 3.2 Product of Unrestricted Trapezoidal Fuzzy Numbers -- 3.2.1 Particular Cases of the Product of Unrestricted Trapezoidal Fuzzy Numbers -- 3.3 Kaur and Kumar's Method for Solving Fully Fuzzy Linear Programming Problems with Equality Constraints -- 3.4 Illustrative Examples -- 3.4.1 Fuzzy Optimal Solution of the Chosen Fully Fuzzy Linear Programming Problems -- 3.5 Advantages of Kaur and Kumar's Method -- 3.6 Real Life Application of Kaur and Kumar's Method -- 3.6.1 Description of the Problem -- 3.7 Comparative Study -- 3.8 Conclusions -- References -- 4 Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constraints Having LR Flat Fuzzy Numbers -- 4.1 Preliminaries -- 4.1.1 Basic Definitions -- 4.1.2 Arithmetic Operations. , 4.2 Product of Unrestricted LR Flat Fuzzy Numbers -- 4.2.1 New Product Corresponding to the Existing Product otimes -- 4.2.2 New Product Corresponding to the Existing Product -- 4.3 Limitations of Previous Presented Method -- 4.4 Kaur and Kumar's Method for Solving Fully Fuzzy Linear Programming Problems with Equality Constraints Having LR Flat Fuzzy Numbers -- 4.5 Illustrative Examples -- 4.5.1 Fuzzy Optimal Solution of the Chosen Fully Fuzzy Linear Programming Problems -- 4.6 Advantages of the Kaur and Kumar's Method -- 4.7 Comparative Study -- 4.8 Conclusions -- References -- 5 Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Inequality Constraints Having LR Flat Fuzzy Numbers -- 5.1 Existing Method for Solving Fully Fuzzy Linear Programming Problems with Inequality Constraints -- 5.2 Applicability of the Existing Methods -- 5.3 Limitations of the Existing Methods -- 5.3.1 Limitations of the Existing Methods for Solving Fuzzy Linear Programming Problems -- 5.3.2 Limitations of the Existing Method for Solving Fully Fuzzy Linear Programming Problems -- 5.4 Kumar and Kaur's Methods for Solving Fully Fuzzy Linear Programming Problems with Inequality Constraints Having LR Flat Fuzzy Numbers -- 5.4.1 Kumar and Kaur's Method -- 5.4.2 Alternative Method -- 5.4.3 Verification of the Presented Methods -- 5.5 Illustrative Example -- 5.5.1 Fuzzy Optimal Solution of the Chosen Problem by Using the Kumar and Kaur's Method -- 5.5.2 Fuzzy Optimal Solution of the Chosen Problem by Using the Alternative Method -- 5.6 Advantages of the Presented Methods -- 5.7 Comparative Study -- 5.8 Conclusions -- References -- 6 Unique Fuzzy Optimal Value of Fully Fuzzy Linear Programming Problems with Equality Constraints Having LR Flat Fuzzy Numbers -- 6.1 Limitations of the Previous Presented Method. , 6.2 Kaur and Kumar's Method Based on RMDS Approach -- 6.2.1 RMDS Approach -- 6.2.2 Kaur and Kumar's Method -- 6.3 Illustrative Example -- 6.4 Advantages of the Kaur and Kumar's Method -- 6.5 Comparative Study -- 6.6 Conclusions -- References -- 7 Future Scope.