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

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.

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.

scholarly journals A comparative study of the methods of solving non-linear programming problem

1970 ◽  
Vol 4 (1) ◽  
pp. 28-34
Author(s):  
Bimal Chandra Das
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Comparative Study ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Region ◽  
Non Linear Programming ◽  
Condition Method ◽  
Non Linear ◽  
Matlab Programming

The work present in this paper is based on a comparative study of the methods of solving Non-linear programming (NLP) problem. We know that Kuhn-Tucker condition method is an efficient method of solving Non-linear programming problem. By using Kuhn-Tucker conditions the quadratic programming (QP) problem reduced to form of Linear programming(LP) problem, so practically simplex type algorithm can be used to solve the quadratic programming problem (Wolfe's Algorithm).We have arranged the materials of this paper in following way. Fist we discuss about non-linear programming problems. In second step we discuss Kuhn- Tucker condition method of solving NLP problems. Finally we compare the solution obtained by Kuhn- Tucker condition method with other methods. For problem so consider we use MATLAB programming to graph the constraints for obtaining feasible region. Also we plot the objective functions for determining optimum points and compare the solution thus obtained with exact solutions. Keywords: Non-linear programming, objective function ,convex-region, pivotal element, optimal solution. DOI: 10.3329/diujst.v4i1.4352 Daffodil International University Journal of Science and Technology Vol.4(1) 2009 pp.28-34

scholarly journals Fully Fuzzy Linear Systems in Python Programming

2020 ◽  
Vol 9 (4) ◽  
pp. 951-956
Keyword(s):  
Linear System ◽  
Fuzzy Number ◽  
Symmetric Matrix ◽  
Triangular Matrix ◽  
New Approach ◽  
Numerical Examples ◽  
Fuzzy Matrix ◽  
Fuzzy Linear System ◽  
Python Programming ◽  
Fuzzy Linear Systems

This paper proposes the python coding for ST decomposition for Triangular, Trapezoidal, and computing the algorithms for the fully fuzzy linear system in python programming. where is a fuzzy matrix, are fuzzy vectors. ST decompose into a product of symmetric matrix (S) and triangular matrix (T) in the form of triangular and trapezoidal fuzzy number matrices. To best illustrate the proposed methods by python coding algorithm with a new approach Python coding has been adopted. Algorithms have been introduced and the numerical examples have been solved by using python techniques. A study of ST decomposition have been done and the solution is obtained with different algorithms. New numerical problems are presented and an example has been solved for this algorithms and the solutions are obtained.

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