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Table of Contents
Intro
Acknowledgements
Contents
About the Authors
1 Introduction
1.1 Origin of More-For-Less Solutions of Transportation Problems
1.2 Literature Review
1.3 Chapter-Wise Summary
References
2 Mehar Method-I to Find All More-For-Less Solutions of Symmetric Fuzzy Balanced Transportation Problems
2.1 Some Basic Definitions
2.2 Tabular Representation of Crisp Balanced Transportation Problems
2.3 Tabular Representation of Symmetric Triangular Fuzzy Balanced Transportation Problems
2.4 Crisp Linear Programming Problems Corresponding to Crisp Balanced Transportation Problems
2.5 Fuzzy Linear Programming Problems Corresponding to Symmetric Triangular Fuzzy Balanced Transportation Problems
2.6 Crisp Balanced Transportation Problems Equivalent to Symmetric Triangular Fuzzy Balanced Transportation Problems
2.7 Proposed Sufficient Condition-I for the Existence of at Least One More-For-Less Solution
2.8 Proposed Mehar Method-I
2.9 Illustrative Examples
2.9.1 All More-For-Less Solutions of an Existing Problem
2.9.2 All More-For-Less Solutions of Considered Problem
2.10 Results and Discussion
2.11 Conclusions
References
3 Mehar Method-II to Find All More-For-Less Solutions of Symmetric Fuzzy Transportation Problems with Mixed Constraints
3.1 Tabular Representation of Crisp Transportation Problems with Mixed Constraints
3.2 Tabular Representation of Symmetric Triangular Fuzzy Transportation Problems with Mixed Constraints
3.3 Crisp Linear Programming Problems Corresponding to Crisp Transportation Problems with Mixed Constraints
3.4 Fuzzy Linear Programming Problems Corresponding to Symmetric Triangular Fuzzy Transportation Problems with Mixed Constraints
3.5 Crisp Transportation Problems with Mixed Constraints Equivalent to Symmetric Triangular Fuzzy Transportation Problems with Mixed Constraints
3.6 Proposed Sufficient Condition-II for the Existence of at Least One More-For-Less Solution
3.7 Proposed Mehar Method-II
3.8 All More-For-Less Solutions of Existing Problems
3.8.1 All More-For-Less Solutions of the First Problem
3.8.2 All More-For-Less Solutions of the Second Problem
3.9 Results and Discussion
3.9.1 Response of the First Question
3.9.2 Response of the Second Question
3.9.3 Response of the Third Question
3.9.4 Response of the Fourth Question
3.10 Conclusions
References
4 Mehar Method-III to Find All More-for-Less Solutions of Symmetric Intuitionistic Fuzzy Transportation Problems with Mixed Constraints
4.1 Some Basic Definitions
4.2 Extended Arithmetic Operations of Triangular Intuitionistic Fuzzy Numbers
4.3 Extended Method for Comparing Triangular Intuitionistic Fuzzy Numbers
4.4 Some Important Results
Acknowledgements
Contents
About the Authors
1 Introduction
1.1 Origin of More-For-Less Solutions of Transportation Problems
1.2 Literature Review
1.3 Chapter-Wise Summary
References
2 Mehar Method-I to Find All More-For-Less Solutions of Symmetric Fuzzy Balanced Transportation Problems
2.1 Some Basic Definitions
2.2 Tabular Representation of Crisp Balanced Transportation Problems
2.3 Tabular Representation of Symmetric Triangular Fuzzy Balanced Transportation Problems
2.4 Crisp Linear Programming Problems Corresponding to Crisp Balanced Transportation Problems
2.5 Fuzzy Linear Programming Problems Corresponding to Symmetric Triangular Fuzzy Balanced Transportation Problems
2.6 Crisp Balanced Transportation Problems Equivalent to Symmetric Triangular Fuzzy Balanced Transportation Problems
2.7 Proposed Sufficient Condition-I for the Existence of at Least One More-For-Less Solution
2.8 Proposed Mehar Method-I
2.9 Illustrative Examples
2.9.1 All More-For-Less Solutions of an Existing Problem
2.9.2 All More-For-Less Solutions of Considered Problem
2.10 Results and Discussion
2.11 Conclusions
References
3 Mehar Method-II to Find All More-For-Less Solutions of Symmetric Fuzzy Transportation Problems with Mixed Constraints
3.1 Tabular Representation of Crisp Transportation Problems with Mixed Constraints
3.2 Tabular Representation of Symmetric Triangular Fuzzy Transportation Problems with Mixed Constraints
3.3 Crisp Linear Programming Problems Corresponding to Crisp Transportation Problems with Mixed Constraints
3.4 Fuzzy Linear Programming Problems Corresponding to Symmetric Triangular Fuzzy Transportation Problems with Mixed Constraints
3.5 Crisp Transportation Problems with Mixed Constraints Equivalent to Symmetric Triangular Fuzzy Transportation Problems with Mixed Constraints
3.6 Proposed Sufficient Condition-II for the Existence of at Least One More-For-Less Solution
3.7 Proposed Mehar Method-II
3.8 All More-For-Less Solutions of Existing Problems
3.8.1 All More-For-Less Solutions of the First Problem
3.8.2 All More-For-Less Solutions of the Second Problem
3.9 Results and Discussion
3.9.1 Response of the First Question
3.9.2 Response of the Second Question
3.9.3 Response of the Third Question
3.9.4 Response of the Fourth Question
3.10 Conclusions
References
4 Mehar Method-III to Find All More-for-Less Solutions of Symmetric Intuitionistic Fuzzy Transportation Problems with Mixed Constraints
4.1 Some Basic Definitions
4.2 Extended Arithmetic Operations of Triangular Intuitionistic Fuzzy Numbers
4.3 Extended Method for Comparing Triangular Intuitionistic Fuzzy Numbers
4.4 Some Important Results