A Solution to a System of Linear Equations with Fuzzy Numbers

2006 ◽  
pp. 417-427
Author(s):  
Xingfang Zhang ◽  
Guangwu Meng
Keyword(s):  
Fuzzy Numbers ◽  
Linear Equations ◽  
System Of Linear Equations

scholarly journals Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Matrix Equation ◽  
Symmetric Solution ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Nonsingular Matrix ◽  
Matrix Equations ◽  
System Of Linear Equations ◽  
Fuzzy Matrix ◽  
Fuzzy Linear System ◽  
Product Of Matrices

The fuzzy symmetric solution of fuzzy matrix equationAX˜=B˜, in whichAis a crispm×mnonsingular matrix andB˜is anm×nfuzzy numbers matrix with nonzero spreads, is investigated. The fuzzy matrix equation is converted to a fuzzy system of linear equations according to the Kronecker product of matrices. From solving the fuzzy linear system, three types of fuzzy symmetric solutions of the fuzzy matrix equation are derived. Finally, two examples are given to illustrate the proposed method.

scholarly journals A QUADRATIC PROGRAMMING MODEL FOR OBTAINING WEAK FUZZY SOLUTION TO FUZZY LINEAR SYSTEMS

2019 ◽  
pp. 381
Author(s):  
Abbas Akrami ◽  
Majid Erfanian
Keyword(s):  
Experimental Data ◽  
Linear Systems ◽  
Optimization Model ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Linear Equations ◽  
Real Life ◽  
System Of Linear Equations ◽  
Fuzzy Solution ◽  
Fuzzy Linear Systems

Real life applications arising in various fields of engineering and science (e.g. electrical, civil, economics, dietary, etc.) can be modelled using a system of linear equations. In such models, it may happen that the values of the parameters are not known or they cannot be stated precisely and that only their estimation due to experimental data or experts knowledge is available. In such a situation it is convenient to represent such parameters by fuzzy numbers. In this paper we propose an efficient optimization model for obtaining a weak fuzzy solution to fuzzy linear systems (FLS). We solve some examples and we show that this method is always efficient.

scholarly journals Approximate Solution ofnth-Order Fuzzy Linear Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Linear Differential

The approximate solution ofnth-order fuzzy linear differential equations in which coefficient functions maintain the sign is investigated by the undetermined fuzzy coefficients method. The differential equations is converted to a crisp function system of linear equations according to the operations of fuzzy numbers. The fuzzy approximate solution of the fuzzy linear differential equation is obtained by solving the crisp linear equations. Some numerical examples are given to illustrate the proposed method. It is an extension of Allahviranloo's results.

scholarly journals Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

2021 ◽  
Author(s):  
David Ek ◽  
Anders Forsgren
Keyword(s):  
Approximate Solution ◽  
Interior Point ◽  
Interior Point Methods ◽  
Linear Equations ◽  
Approximate Solutions ◽  
System Of Nonlinear Equations ◽  
Intermediate Step ◽  
System Of Linear Equations ◽  
Constrained Nonlinear Optimization ◽  
Asymptotic Error

AbstractThe focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton’s method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework.

scholarly journals Numerical approximation for the solution of linear sixth order boundary value problems by cubic B-spline

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. Khalid ◽  
M. N. Naeem ◽  
P. Agarwal ◽  
A. Ghaffar ◽  
Z. Ullah ◽  
...  
Keyword(s):  
Numerical Approximation ◽  
Analytic Solution ◽  
Linear Equations ◽  
Computational Cost ◽  
Spline Method ◽  
System Of Linear Equations ◽  
Approximation Solution ◽  
B Spline ◽  
Novel Technique ◽  
Derivatives Of

AbstractIn the current paper, authors proposed a computational model based on the cubic B-spline method to solve linear 6th order BVPs arising in astrophysics. The prescribed method transforms the boundary problem to a system of linear equations. The algorithm we are going to develop in this paper is not only simply the approximation solution of the 6th order BVPs using cubic B-spline, but it also describes the estimated derivatives of 1st order to 6th order of the analytic solution at the same time. This novel technique has lesser computational cost than numerous other techniques and is second order convergent. To show the efficiency of the proposed method, four numerical examples have been tested. The results are described using error tables and graphs and are compared with the results existing in the literature.

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