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E-raamat: Introduction to Fuzzy Linear Programming Problems: Theory, Methods and Applications

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Introduction to Fuzzy Linear Programming Problems: Theory, Methods and ApplicationsSuurem pilt
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The book presents a snapshot of the state of the art in the field of fully fuzzy linear programming. The main focus is on showing current methods for finding the fuzzy optimal solution of fully fuzzy linear programming problems in which all the parameters and decision variables are represented by non-negative fuzzy numbers.  It presents new methods developed by the authors, as well as existing methods developed by others, and their application to real-world problems, including fuzzy transportation problems. Moreover, it compares the outcomes of the different methods and discusses their advantages/disadvantages. As the first work to collect at one place the most important methods for solving fuzzy linear programming problems, the book represents a useful reference guide for students and researchers, providing them with the necessary theoretical and practical knowledge to deal with linear programming problems under uncertainty.
1 State of the Art
1(14)
References
9(6)
2 Non-negative Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constraints
15(20)
2.1 Preliminaries
15(3)
2.1.1 Basic Definitions
15(2)
2.1.2 Arithmetic Operations
17(1)
2.2 Existing Method for Solving Fully Fuzzy Linear Programming Problems with Equality Constraints
18(2)
2.3 Limitations and Shortcoming of the Existing Method
20(2)
2.3.1 Limitations of the Existing Method
20(2)
2.3.2 Shortcoming of the Existing Method
22(1)
2.4 Product of a Non-negative Trapezoidal Fuzzy Number with Unrestricted Trapezoidal Fuzzy Number
22(1)
2.5 Kumar et al.'s Method to Find the Non-negative Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constraints
23(4)
2.6 Illustrative Examples
27(5)
2.6.1 Fuzzy Optimal Solution of the Chosen Fully Fuzzy Linear Programming Problems
27(5)
2.7 Advantages of the Kumar et al.'s Method
32(1)
2.8 Comparative Study
33(1)
2.9 Conclusions
33(2)
References
34(1)
3 Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constrains
35(20)
3.1 Limitations of the Previous Presented Method
35(2)
3.2 Product of Unrestricted Trapezoidal Fuzzy Numbers
37(1)
3.2.1 Particular Cases of the Product of Unrestricted Trapezoidal Fuzzy Numbers
37(1)
3.3 Kaur and Kumar's Method for Solving Fully Fuzzy Linear Programming Problems with Equality Constraints
38(4)
3.4 Illustrative Examples
42(8)
3.4.1 Fuzzy Optimal Solution of the Chosen Fully Fuzzy Linear Programming Problems
42(8)
3.5 Advantages of Kaur and Kumar's Method
50(1)
3.6 Real Life Application of Kaur and Kumar's Method
50(3)
3.6.1 Description of the Problem
51(2)
3.7 Comparative Study
53(1)
3.8 Conclusions
53(2)
References
54(1)
4 Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constraints Having LR Flat Fuzzy Numbers
55(22)
4.1 Preliminaries
55(3)
4.1.1 Basic Definitions
56(1)
4.1.2 Arithmetic Operations
57(1)
4.2 Product of Unrestricted LR Flat Fuzzy Numbers
58(6)
4.2.1 New Product Corresponding to the Existing Product ⊗
58(4)
4.2.2 New Product Corresponding to the Existing Product
62(2)
4.3 Limitations of Previous Presented Method
64(1)
4.4 Kaur and Kumar's Method for Solving Fully Fuzzy Linear Programming Problems with Equality Constraints Having LR Flat Fuzzy Numbers
65(4)
4.5 Illustrative Examples
69(5)
4.5.1 Fuzzy Optimal Solution of the Chosen Fully Fuzzy Linear Programming Problems
69(5)
4.6 Advantages of the Kaur and Kumar's Method
74(1)
4.7 Comparative Study
74(1)
4.8 Conclusions
75(2)
References
75(2)
5 Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Inequality Constraints Having LR Flat Fuzzy Numbers
77(32)
5.1 Existing Method for Solving Fully Fuzzy Linear Programming Problems with Inequality Constraints
77(2)
5.2 Applicability of the Existing Methods
79(3)
5.3 Limitations of the Existing Methods
82(5)
5.3.1 Limitations of the Existing Methods for Solving Fuzzy Linear Programming Problems
83(3)
5.3.2 Limitations of the Existing Method for Solving Fully Fuzzy Linear Programming Problems
86(1)
5.4 Kumar and Kaur's Methods for Solving Fully Fuzzy Linear Programming Problems with Inequality Constraints Having LR Flat Fuzzy Numbers
87(13)
5.4.1 Kumar and Kaur's Method
87(7)
5.4.2 Alternative Method
94(4)
5.4.3 Verification of the Presented Methods
98(2)
5.5 Illustrative Example
100(6)
5.5.1 Fuzzy Optimal Solution of the Chosen Problem by Using the Kumar and Kaur's Method
100(3)
5.5.2 Fuzzy Optimal Solution of the Chosen Problem by Using the Alternative Method
103(3)
5.6 Advantages of the Presented Methods
106(1)
5.7 Comparative Study
106(2)
5.8 Conclusions
108(1)
References
108(1)
6 Unique Fuzzy Optimal Value of Fully Fuzzy Linear Programming Problems with Equality Constraints Having LR Flat Fuzzy Numbers
109(10)
6.1 Limitations of the Previous Presented Method
109(1)
6.2 Kaur and Kumar's Method Based on RMDS Approach
110(4)
6.2.1 RMDS Approach
110(1)
6.2.2 Kaur and Kumar's Method
111(3)
6.3 Illustrative Example
114(3)
6.4 Advantages of the Kaur and Kumar's Method
117(1)
6.5 Comparative Study
117(1)
6.6 Conclusions
117(2)
References
118(1)
7 Future Scope
119
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