scholarly journals Software for Solving Fully Fuzzy Linear Systems with Rectangular Matrix

2020 ◽  
Vol 10 (1) ◽  
pp. 129-139
Author(s):  
A.V. Panteleev ◽  
V.S. Saveleva
Keyword(s):  
Linear Systems ◽  
Linear Equations ◽  
Linear System Of Equations ◽  
Software Application ◽  
Rectangular Matrix ◽  
Fuzzy Linear System ◽  
Triangular Numbers ◽  
Systems Of Linear Equations ◽  
The Mean ◽  
Fuzzy Linear Systems

The article discusses the problem of solving a fully fuzzy linear system of equations with a fuzzy rectangular matrix and a fuzzy right-hand side described by fuzzy triangular numbers in a form of deviations from the mean. A solution algorithm based on finding pseudo-solutions of systems of linear equations and corresponding software is formed. Various examples of created software application for arbitrary fuzzy linear systems are given.

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 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.

The Back Page: My Favorite Lesson: Unfolding the Solution of Linear Systems

2010 ◽  
Vol 104 (2) ◽  
pp. 160
Author(s):  
Sarah B. Bush
Keyword(s):  
Linear Systems ◽  
Student Teaching ◽  
Linear Equations ◽  
Teaching Experience ◽  
Correct Solution ◽  
First Year ◽  
Know How ◽  
Big Picture ◽  
Systems Of Linear Equations ◽  
Algebra Class

I often think back to a vivid memory from my student-teaching experience. Then, I naively believed that the weeks spent with my first-year algebra class discussing and practicing the art of solving systems of linear equations by graphing, substitution, and elimination was a success. But just at that point the students started asking revealing questions such as “How do you know which method to pick so that you get the correct solution?” and “Which systems go with which methods?” I then realized that my instruction had failed to guide my students toward conceptualizing the big picture of linear systems and instead had left them with a procedure they did not know how to apply. At that juncture I decided to try this discovery-oriented lesson.

scholarly journals General Solutions of Fully Fuzzy Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
T. Allahviranloo ◽  
S. Salahshour ◽  
M. Homayoun-nejad ◽  
D. Baleanu
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Solution Set ◽  
Solution Sets ◽  
General Solutions ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System ◽  
Fuzzy Linear Systems

We propose a method to approximate the solutions of fully fuzzy linear system (FFLS), the so-calledgeneral solutions. So, we firstly solve the 1-cut position of a system, then some unknown spreads are allocated to each row of an FFLS. Using this methodology, we obtain some general solutions which are placed in the well-known solution sets like Tolerable solution set (TSS) and Controllable solution set (CSS). Finally, we solved two examples in order to demonstrate the ability of the proposed method.

Accelerated GPMHSS Method for Solving Complex Systems of Linear Equations

2017 ◽  
Vol 7 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Jing Wang ◽  
Xue-Ping Guo ◽  
Hong-Xiu Zhong
Keyword(s):  
Complex Systems ◽  
Linear Systems ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Splitting Method ◽  
Complex Symmetric Linear Systems ◽  
Systems Of Linear Equations ◽  
Complex Symmetric ◽  
Symmetric Systems

AbstractPreconditioned modified Hermitian and skew-Hermitian splitting method (PMHSS) is an unconditionally convergent iteration method for solving large sparse complex symmetric systems of linear equations, and uses one parameter α. Adding another parameter β, the generalized PMHSS method (GPMHSS) is essentially a twoparameter iteration method. In order to accelerate the GPMHSS method, using an unexpected way, we propose an accelerated GPMHSS method (AGPMHSS) for large complex symmetric linear systems. Numerical experiments show the numerical behavior of our new method.

scholarly journals Accelerating advanced preconditioning methods on hybrid architectures

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Ernesto Dufrechou
Keyword(s):  
Linear Systems ◽  
Large Scale ◽  
Krylov Subspace ◽  
Linear Equations ◽  
Memory Systems ◽  
Sparse Linear Systems ◽  
Data Parallel ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Computational Bottleneck

Many problems, in diverse areas of science and engineering, involve the solution of largescale sparse systems of linear equations. In most of these scenarios, they are also a computational bottleneck, and therefore their efficient solution on parallel architectureshas motivated a tremendous volume of research.This dissertation targets the use of GPUs to enhance the performance of the solution of sparse linear systems using iterative methods complemented with state-of-the-art preconditioned techniques. In particular, we study ILUPACK, a package for the solution of sparse linear systems via Krylov subspace methods that relies on a modern inverse-based multilevel ILU (incomplete LU) preconditioning technique.We present new data-parallel versions of the preconditioner and the most important solvers contained in the package that significantly improve its performance without affecting its accuracy. Additionally we enhance existing task-parallel versions of ILUPACK for shared- and distributed-memory systems with the inclusion of GPU acceleration. The results obtained show a sensible reduction in the runtime of the methods, as well as the possibility of addressing large-scale problems efficiently.

scholarly journals A note on “The nearest symmetric fuzzy solution for a symmetric fuzzy linear system”

2015 ◽  
Vol 23 (2) ◽  
pp. 173-177 ◽  
Author(s):  
Ghassan Malkawi ◽  
Nazihah Ahmad ◽  
Haslinda Ibrahim
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Approximate Solutions ◽  
Fuzzy Linear System ◽  
Fuzzy Solution ◽  
Fuzzy Linear Systems

Abstract This paper provides accurate approximate solutions for the symmetric fuzzy linear systems in (Allahviranloo et al:[1]).

Planning for Hurricane Isaac using Probability Theory in a Linear Programming Model

2013 ◽  
pp. 1056-1072
Author(s):  
Kenneth David Strang
Keyword(s):  
Probability Theory ◽  
Linear Programming ◽  
Hurricane Katrina ◽  
Programming Model ◽  
Linear Equations ◽  
Disaster Planning ◽  
Planning Methods ◽  
Systems Of Linear Equations ◽  
The Mean

The author demonstrated how linear programming (LP) models with embedded probability theory were applied for disaster planning to mitigate the damages of hurricane Isaac. The purpose of the article was to raise awareness of software-based disaster planning methods, and to demonstrate how uncertainty can be quantified as risk estimates to substitute for and then added as constraints in LP models. Several LP approaches and alternatives were reviewed from the literature. Three LP problem-solving techniques were demonstrated: graphing, algebraic systems of linear equations, and using spreadsheet software. Two disaster planning LP models were solved based on the Federal Emergency Management Agency case study of hurricane Isaac in 2012. The case study focused on allocating emergency supplies to strategic Point of Distribution locations. A unique feature of the article was showing how uncertainty could be quantified as risk by calculating the mean, standard deviation and coefficient of variation for airboat trips based on historical data from hurricane Katrina. Several insights of LP model formulation were given to assist others.

PARALLEL ITERATIVE REGULARIZATION ALGORITHMS FOR LARGE OVERDETERMINED LINEAR SYSTEMS

2010 ◽  
Vol 07 (04) ◽  
pp. 525-537 ◽  
Author(s):  
PHAM KY ANH ◽  
VU TIEN DUNG
Keyword(s):  
Linear Systems ◽  
Linear Equations ◽  
Regularization Methods ◽  
Iterative Regularization ◽  
Overdetermined Systems ◽  
Overdetermined Linear Systems ◽  
Systems Of Linear Equations ◽  
Parallel Iterative

In this paper, we study the performance of some parallel iterative regularization methods for solving large overdetermined systems of linear equations.

Modified Iterative Methods for Solving Fully Fuzzy Linear Systems

Fuzzy Systems ◽  
2017 ◽  
pp. 55-73
Author(s):  
S. A. Edalatpanah
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Fuzzy System ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Numerical Procedure ◽  
Numerical Results ◽  
System Of Linear Equations ◽  
Iterative Schemes ◽  
Fuzzy Linear Systems

In the present chapter, we give an overview of computational iterative schemes for fuzzy system of linear equations. We also consider fully fuzzy linear systems (FFLS) and demonstrate a class of the existing iterative methods using the splitting approach for calculating the solution. Furthermore, the main aim in this work is to design a numerical procedure for improving this algorithm. Some numerical experiments are illustrated to show the applicability of the methods and to show the efficiency of proposed algorithm, we report the numerical results of large-scaled fuzzy problems.

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