A new computational method to solve fully fuzzy linear systems for negative coefficient matrix

2012 ◽  
Vol 25 (1/2/3) ◽  
pp. 19 ◽  
Author(s):  
Amit Kumar ◽  
Neetu Babbar ◽  
Abhinav Bansal
Keyword(s):  
Linear Systems ◽  
Coefficient Matrix ◽  
Computational Method ◽  
Negative Coefficient ◽  
Fuzzy Linear Systems

scholarly journals H-Matrices in Fuzzy Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Saberi Najafi ◽  
S. A. Edalatpanah
Keyword(s):  
Linear System ◽  
Theoretical Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
System Of Equations ◽  
Linear System Of Equations ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

We consider a class of fuzzy linear system of equations and demonstrate some of the existing challenges. Furthermore, we explain the efficiency of this model when the coefficient matrix is an H-matrix. Numerical experiments are illustrated to show the applicability of the theoretical analysis.

scholarly journals A Relaxed Kaczmarz Method for Fuzzy Linear Systems

2021 ◽  
Author(s):  
Ke Wang ◽  
Shijun Zhang ◽  
Shiheng Wang
Keyword(s):  
Linear Systems ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Coefficient Matrix ◽  
Systems Of Equations ◽  
Numerical Examples ◽  
Right Hand ◽  
Kaczmarz Method ◽  
Fuzzy Linear Systems ◽  
Linear Systems Of Equations

Abstract A relaxed Kaczmarz method is presented for solving a class of fuzzy linear systems of equations with crisp coefficient matrix and fuzzy right-hand side. The iterative scheme is established and the convergence theorem is provided. Numerical examples show that the method is effective.

scholarly journals A New Approach for Solving Fully Fuzzy Linear Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Amit Kumar ◽  
Neetu ◽  
Abhinav Bansal
Keyword(s):  
Linear Systems ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Primary Objective ◽  
Computational Method ◽  
Solution Vector ◽  
New Approach ◽  
Fuzzy Variables ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

Several authors have proposed different methods to find the solution of fully fuzzy linear systems (FFLSs) that is, fuzzy linear system with fuzzy coefficients involving fuzzy variables. But all the existing methods are based on the assumption that all the fuzzy coefficients and the fuzzy variables are nonnegative fuzzy numbers. In this paper a new method is proposed to solve an FFLS with arbitrary coefficients and arbitrary solution vector, that is, there is no restriction on the elements that have been used in the FFLS. The primary objective of this paper is thus to introduce the concept and a computational method for solving FFLS with no non negative constraint on the parameters. The method incorporates the principles of linear programming in solving an FFLS with arbitrary coefficients and is not only easier to understand but also widens the scope of fuzzy linear equations in scientific applications. To show the advantages of the proposed method over existing methods we solve three FFLSs.

Methods for solving LR-bipolar fuzzy linear systems

2021 ◽  
Author(s):  
Muhammad Akram ◽  
Tofigh Allahviranloo ◽  
Witold Pedrycz ◽  
Muhammad Ali
Keyword(s):  
Linear Systems ◽  
Fuzzy Linear Systems

scholarly journals On the fuzzy solution of LR fuzzy linear systems

2013 ◽  
Vol 37 (3) ◽  
pp. 1170-1176 ◽  
Author(s):  
T. Allahviranloo ◽  
F. Hosseinzadeh Lotfi ◽  
M. Khorasani Kiasari ◽  
M. Khezerloo
Keyword(s):  
Linear Systems ◽  
Fuzzy Solution ◽  
Fuzzy Linear Systems

Nondegenerate Piecewise Linear Systems: A Finite Newton Algorithm and Applications in Machine Learning

2012 ◽  
Vol 24 (4) ◽  
pp. 1047-1084 ◽  
Author(s):  
Xiao-Tong Yuan ◽  
Shuicheng Yan
Keyword(s):  
Linear Systems ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Optimization Methods ◽  
Coefficient Matrix ◽  
Learning Problems ◽  
Support Vector ◽  
Data Sets ◽  
Piecewise Linear Systems ◽  
Vector Machines

We investigate Newton-type optimization methods for solving piecewise linear systems (PLSs) with nondegenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem, which is useful to model several learning and optimization problems. In this letter, we propose an effective damped Newton method, PLS-DN, to find the exact (up to machine precision) solution of nondegenerate PLSs. PLS-DN exhibits provable semiiterative property, that is, the algorithm converges globally to the exact solution in a finite number of iterations. The rate of convergence is shown to be at least linear before termination. We emphasize the applications of our method in modeling, from a novel perspective of PLSs, some statistical learning problems such as box-constrained least squares, elitist Lasso (Kowalski & Torreesani, 2008 ), and support vector machines (Cortes & Vapnik, 1995 ). Numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of PLS-DN on these problems.

Solving fuzzy linear systems using a block representation of generalized inverses: The group inverse

2018 ◽  
Vol 353 ◽  
pp. 66-85 ◽  
Author(s):  
Biljana Mihailović ◽  
Vera Miler Jerković ◽  
Branko Malešević
Keyword(s):  
Linear Systems ◽  
Generalized Inverses ◽  
Group Inverse ◽  
Fuzzy Linear Systems

Fuzzy linear systems

1992 ◽  
Vol 49 (3) ◽  
pp. 339-355 ◽  
Author(s):  
Ketty Peeva
Keyword(s):  
Linear Systems ◽  
Fuzzy Linear Systems
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