LU Decomposition method to solve bipolar fuzzy linear systems

2020 ◽  
Vol 39 (3) ◽  
pp. 3329-3349 ◽  
Author(s):  
Muhammad Akram ◽  
Ghulam Muhammad ◽  
Tofigh Allahviranloo ◽  
Nawab Hussain
Keyword(s):  
Decomposition Method ◽  
Matrix Theory ◽  
Coefficient Matrix ◽  
Least Square ◽  
Lu Decomposition ◽  
Fuzzy Matrix ◽  
Linear System Of Equations ◽  
Fuzzy Environment ◽  
Generalized Inverse Matrix ◽  
Fuzzy Linear Systems

The aim of this work is to solve the linear system of equations using LU decomposition method in bipolar fuzzy environment. We assume a special case when the coefficient matrix of the system is symmetric positive definite. We discuss this point in detail by giving some numerical examples. Moreover, we investigate m × n inconsistent bipolar fuzzy matrix equation and find the least square solution of the inconsistent bipolar fuzzy matrix using the generalized inverse matrix theory. The existence of the strong bipolar fuzzy least square solution of the inconsistent bipolar fuzzy matrix is discussed. In the end, a numerical example is presented to illustrate our proposed method.

scholarly journals LU Decomposition Scheme for Solving m-Polar Fuzzy System of Linear Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-19 ◽  
Author(s):  
Ali N. A. Koam ◽  
Muhammad Akram ◽  
Ghulam Muhammad ◽  
Nawab Hussain
Keyword(s):  
Fuzzy System ◽  
Matrix Theory ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Least Square ◽  
System Of Linear Equations ◽  
Fuzzy Matrix ◽  
Decomposition Scheme ◽  
Symmetric Positive Definite ◽  
Generalized Inverse Matrix

This paper presents a new scheme for solving m-polar fuzzy system of linear equations (m-PFSLEs) by using LU decomposition method. We assume the coefficient matrix of the system is symmetric positive definite, and we discuss this point in detail with some numerical examples. Furthermore, we investigate the inconsistent m×nm-polar fuzzy matrix equation (m-PFME) and find the least square solution (LSS) of this system by using generalized inverse matrix theory. Moreover, we discuss the strong solution of m-polar fuzzy LSS of the inconsistent m-PFME. In the end, we present a numerical example to illustrate our approach.

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.

Civil Aeroengine Fault Diagnosis Based on Fuzzy Least Square Support Vector Machine

2011 ◽  
Vol 130-134 ◽  
pp. 2047-2050 ◽  
Author(s):  
Hong Chun Qu ◽  
Xie Bin Ding
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Support Vector Machine ◽  
Fault Diagnosis ◽  
Coefficient Matrix ◽  
Least Square ◽  
Support Vector ◽  
Influence Coefficient ◽  
Structural Risk ◽  
Better Than

SVM(Support Vector Machine) is a new artificial intelligence methodolgy, basing on structural risk mininization principle, which has better generalization than the traditional machine learning and SVM shows powerfulability in learning with limited samples. To solve the problem of lack of engine fault samples, FLS-SVM theory, an improved SVM, which is a method is applied. 10 common engine faults are trained and recognized in the paper.The simulated datas are generated from PW4000-94 engine influence coefficient matrix at cruise, and the results show that the diagnostic accuracy of FLS-SVM is better than LS-SVM.

scholarly journals Generalized Euclidean Least Square Approximation

2018 ◽  
pp. 1-10
Author(s):  
A. S. Oke ◽  
S. M. Akintewe ◽  
A. G. Akinbande
Keyword(s):  
Exponential Function ◽  
Existence And Uniqueness ◽  
Coefficient Matrix ◽  
Least Square ◽  
Data Set ◽  
Condensation Method ◽  
The Matrix

A Generalised Euclidean Least Square Approximation (ELS) is derived in this paper. The Generalised Euclidean Least Square Approximation is derived by generalizing the interpolation of n arbitrary data set to approximate functions. Existence and uniqueness of the ELS schemes are shown by establishing the invertibility of the coefficient matrix using condensation method to reduce the matrix. The method is illustrated for exponential function and the results are compared to the classical Maclaurin’s series.

scholarly journals HotSpot Thermal Floorplan Solver Using Conjugate Gradient to Speed Up

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Zhonghua Jiang ◽  
Ning Xu
Keyword(s):  
Simulated Annealing ◽  
Conjugate Gradient ◽  
Decomposition Method ◽  
Sparse Matrix ◽  
Lu Decomposition ◽  
Ratio Curve ◽  
Resistance Model ◽  
Speed Up ◽  
Iterative Framework ◽  
Conjugate Gradient Solver

We proposed to use the conjugate gradient method to effectively solve the thermal resistance model in HotSpot thermal floorplan tool. The iterative conjugate gradient solver is suitable for traditional sparse matrix linear systems. We also defined the relative sparse matrix in the iterative thermal floorplan of Simulated Annealing framework algorithm, and the iterative method of relative sparse matrix could be applied to other iterative framework algorithms. The experimental results show that the running time of our incremental iterative conjugate gradient solver is speeded up approximately 11x compared with the LU decomposition method for case ami49, and the experiment ratio curve shows that our iterative conjugate gradient solver accelerated more with increasing number of modules.

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