scholarly journals A Proposed Method for Solving Fuzzy System of Linear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Reza Kargar ◽  
Tofigh Allahviranloo ◽  
Mohsen Rostami-Malkhalifeh ◽  
Gholam Reza Jahanshaloo
Keyword(s):  
Linear Programming ◽  
Linear System ◽  
Programming Problem ◽  
Fuzzy System ◽  
Linear Programming Problem ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Interval Solution ◽  
Practical Algorithm

This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution ofm×nlinear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.

Certain efficient iterative methods for bipolar fuzzy system of linear equations

2020 ◽  
Vol 39 (3) ◽  
pp. 3971-3985 ◽  
Author(s):  
Muhammad Saqib ◽  
Muhammad Akram ◽  
Shahida Bashir
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Iterative Methods ◽  
Fuzzy Set ◽  
Fuzzy System ◽  
Linear Equations ◽  
Performance Validity ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Iterative Schemes

A bipolar fuzzy set model is an extension of fuzzy set model. We develop new iterative methods: generalized Jacobi, generalized Gauss-Seidel, refined Jacobi, refined Gauss-seidel, refined generalized Jacobi and refined generalized Gauss-seidel methods, for solving bipolar fuzzy system of linear equations(BFSLEs). We decompose n ×  n BFSLEs into 4n ×  4n symmetric crisp linear system. We present some results that give the convergence of proposed iterative methods. We solve some BFSLEs to check the validity, efficiency and stability of our proposed iterative schemes. Further, we compute Hausdorff distance between the exact solutions and approximate solution of our proposed schemes. The numerical examples show that some proposed methods converge for the BFSLEs, but Jacobi and Gauss-seidel iterative methods diverge for BFSLEs. Finally, comparison tables show the performance, validity and efficiency of our proposed iterative methods for BFSLEs.

scholarly journals The nearest symmetric fuzzy solution for a symmetric fuzzy linear system

2012 ◽  
Vol 20 (1) ◽  
pp. 151-172 ◽  
Author(s):  
T. Allahviranloo ◽  
E. Haghi ◽  
M. Ghanbari
Keyword(s):  
Linear Programming ◽  
Linear System ◽  
Programming Problem ◽  
Fuzzy Number ◽  
Linear Programming Problem ◽  
Vector Solution ◽  
Numerical Examples ◽  
Non Linear Programming ◽  
Fuzzy Linear System ◽  
Fuzzy Solution

Abstract In this paper, the nearest symmetric fuzzy solution for a symmetric L-L fuzzy linear system (S-L-FLS) is obtained by a new metric. To this end, the S-L-FLS is transformed to the non-linear programming problem (NLP). The solution of the obtained NLP is our favorite fuzzy number vector solution. Also, it is shown that if an S-L-FLS has unique fuzzy solution, then its solution is symmetric. Two constructive algorithms are presented in details and the method is illustrated by solving several numerical examples

Construction Method of Constraint Matrices Corresponded by an Optimal Solution

2014 ◽  
Vol 513-517 ◽  
pp. 1617-1620
Author(s):  
Xiao Liu ◽  
Wei Li ◽  
Peng Zhen Liu
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Linear Equations ◽  
Optimal Solution ◽  
Construction Method ◽  
Interval Linear Programming ◽  
Interval Linear

Through deep analysis of the solvability, which is based on interval linear equations and inequalities systems, for a given optimal solution to interval linear programming problem, we propose the construction method of constraint matrices corresponded by the optimal solution in this paper.

scholarly journals A Novel Technique to Solve the Fuzzy System of Equations

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 850
Author(s):  
Nasser Mikaeilvand ◽  
Zahra Noeiaghdam ◽  
Samad Noeiaghdam ◽  
Juan J. Nieto
Keyword(s):  
Linear System ◽  
Fuzzy Number ◽  
Fuzzy System ◽  
Linear Equations ◽  
Second Step ◽  
Negative Solution ◽  
System Of Linear Equations ◽  
Vector Solution ◽  
Novel Technique ◽  
Fuzzy Linear System

The aim of this research is to apply a novel technique based on the embedding method to solve the n × n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created n × n crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created n × n crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors.

Solutions of Fuzzy System of Linear Equations

2020 ◽  
pp. 26-33
Author(s):  
Laxminarayan Sahoo
Keyword(s):  
Linear System ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Number ◽  
Fuzzy System ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Interval System ◽  
Solution Methodology

This chapter deals with solution methodology of fuzzy system of linear equations (FSLEs). In fuzzy set theory, finding solutions of FLSEs has long been a well-known problem to the researchers. In this chapter, the fuzzy number has been converted into interval number, and the authors have solved the interval system of linear equation for finding the fuzzy valued solution. Here, a fuzzy valued linear system has been introduced and a numerical example has been solved and presented for illustration of purpose.

scholarly journals A New Method for Optimal Solutions of Transportation Problems in LPP

2018 ◽  
Vol 10 (5) ◽  
pp. 60
Author(s):  
Muhammad Hanif ◽  
Farzana Sultana Rafi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Optimal Solution ◽  
New Method ◽  
Optimal Solutions ◽  
Attractive Feature ◽  
Numerical Examples ◽  
Transportation Problems ◽  
Clear Idea

The several standard and the existing proposed methods for optimality of transportation problems in linear programming problem are available. In this paper, we considered all standard and existing proposed methods and then we proposed a new method for optimal solution of transportation problems. The most attractive feature of this method is that it requires very simple arithmetical and logical calculation, that’s why it is very easy even for layman to understand and use. Some limitations and recommendations of future works are also mentioned of the proposed method. Several numerical examples have been illustrated, those gives the clear idea about the method. A programming code for this method has been written in Appendix of the paper.

scholarly journals Optimization of LR -Type Fully Bipolar Fuzzy Linear Programming Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-36
Author(s):  
Muhammad Athar Mehmood ◽  
Muhammad Akram ◽  
Majed G. Alharbi ◽  
Shahida Bashir
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Equality Constraints ◽  
Fuzzy Linear Programming ◽  
Numerical Examples ◽  
Linear Programming Problems ◽  
Formula Type ◽  
Crisp Linear Programming

In this study, we present a technique to solve LR -type fully bipolar fuzzy linear programming problems (FBFLPPs) with equality constraints. We define LR -type bipolar fuzzy numbers and their arithmetic operations. We discuss multiplication of LR -type bipolar fuzzy numbers. Furthermore, we develop a method to solve LR -type FBFLPPs with equality constraints involving LR -type bipolar fuzzy numbers as parameters and variables. Moreover, we define ranking for LR -type bipolar fuzzy numbers which transform the LR -type FBFLPP into a crisp linear programming problem. Finally, we consider numerical examples to illustrate the proposed method.

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