This book describes a set of methods for finding more-for-less solutions of various kind of fuzzy transportation problems. Inspired by more-for-less approaches to the basic transportation problem initiated by Abraham Charnes and his collaborators during 1960s and 1970s, this book describes new methods developed by the authors to solve different types of problems, including symmetric balanced fuzzy transportation problems, symmetric intuitionistic fuzzy transportation problems with mixed constraints, and symmetric intuitionistic fuzzy linear fractional transportation problems with mixed constraints. It offers extensive details on their applications to some representative problems, and discusses some future research directions
Author(s): Tanveen Kaur Bhatia, Amit Kumar, Srimantoorao S. Appadoo
Series: Studies in Fuzziness and Soft Computing, 426
Publisher: Springer
Year: 2023
Language: English
Pages: 168
City: Cham
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
4.4.1 Proof of the First Result
4.4.2 Proof of the Second Result
4.4.3 Proof of the Third Result
4.4.4 Proof of the Fourth Result
4.5 Tabular Representation of Symmetric Triangular Intuitionistic Fuzzy Transportation Problems with Mixed Constraints
4.6 Intuitionistic Fuzzy Linear Programming Problems Corresponding to Symmetric Triangular Intuitionistic Fuzzy Transportation Problems with Mixed Constraints
4.7 Crisp Transportation Problem Equivalent to Symmetric Intuitionistic Fuzzy Transportation Problem
4.8 Proposed Sufficient Condition-III for the Existence of at Least One More-for-Less Solution
4.9 Proposed Mehar Method-III
4.10 Illustrative Example
4.11 Conclusions
References
5 Mehar Method-IV to Find All More-For-Less Solutions of Symmetric Intuitionistic Fuzzy Linear Fractional Transportation Problems with Mixed Constraints
5.1 Tabular Representation of Crisp Linear Fractional Transportation Problems with Mixed Constraints
5.2 Tabular Representation of Symmetric Triangular Intuitionistic Fuzzy Linear Fractional Transportation Problems with Mixed Constraints
5.3 Crisp Linear Fractional Programming Problems Corresponding to Crisp Linear Fractional Transportation Problem with Mixed Constraints
5.4 Intuitionistic Fuzzy Linear Fractional Programming Problems Corresponding to Symmetric Triangular Intuitionistic Fuzzy Linear Fractional Transportation Problem with Mixed Constraints
5.5 Crisp Linear Fractional Transportation Problem with Mixed Constraints Equivalent to Symmetric Triangular Intuitionistic Fuzzy Linear Fractional Transportation Problem with Mixed Constraints
5.6 Proposed Sufficient Condition-IV for the Existence of at Least One More-For-Less Solution
5.6.1 Origin of the Sufficient Condition (5.1a)
5.6.2 Origin of the Sufficient Condition (5.1b)
5.7 Proposed Mehar Method-IV
5.8 Illustrative Examples
5.8.1 All More-For-Less Solutions of the First Existing Problem
5.8.2 All More-For-Less Solutions of the Second Existing Problem
5.8.3 All More-For-Less Solutions of the Considered Problem
5.9 Results and Discussion
5.9.1 Response of the First Question
5.9.2 Response of the Second Question
5.10 Conclusions
References
6 Some Open Research Problems
6.1 First Open Research Problem
6.2 Second Open Research Problem
6.3 Third Open Research Problem
6.4 Fourth Open Research Problem
6.5 Fifth Open Research Problem
References
