scholarly journals Approximate Solution of Fuzzy Matrix Equations with LR Fuzzy Numbers

2012 ◽  
Vol 02 (06) ◽  
pp. 373-378 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Approximate Solution ◽  
Fuzzy Numbers ◽  
Matrix Equations ◽  
Fuzzy Matrix

scholarly journals Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Approximate Solution ◽  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Existence Condition ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Arithmetic Operations ◽  
Fuzzy Matrix ◽  
Fuzzy Solution ◽  
Linear Matrix Equations

The fuzzy matrix equationsA~⊗X~⊗B~=C~in whichA~,B~, andC~arem×m,n×n, andm×nnonnegative LR fuzzy numbers matrices, respectively, are investigated. The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to arithmetic operations of LR fuzzy numbers. Based on pseudoinverse of matrix, the fuzzy approximate solution of original fuzzy systems is obtained by solving the crisp linear matrix systems. In addition, the existence condition of nonnegative fuzzy solution is discussed. Two examples are calculated to illustrate the proposed method.

Approximate solution of dual fuzzy matrix equations

2014 ◽  
Vol 266 ◽  
pp. 112-133 ◽  
Author(s):  
Zengtai Gong ◽  
Xiaobin Guo ◽  
Kun Liu
Keyword(s):  
Approximate Solution ◽  
Matrix Equations ◽  
Fuzzy Matrix

scholarly journals Approximate Solution of LR Fuzzy Sylvester Matrix Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Matrix Equation ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Existence Condition ◽  
Sylvester Matrix Equation ◽  
Fuzzy Matrix ◽  
Sylvester Matrix ◽  
Fuzzy Linear System

The fuzzy Sylvester matrix equationAX~+X~B=C~in whichA,Barem×mandn×ncrisp matrices, respectively, andC~is anm×nLR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

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 Solving Complex Fuzzy Linear Matrix Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yirong Sun ◽  
Junyang An ◽  
Xiaobin Guo
Keyword(s):  
Matrix Equation ◽  
Fuzzy Numbers ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Linear Matrix Equation ◽  
Fuzzy Matrix ◽  
System Of Matrix Equations ◽  
Fuzzy Solution ◽  
Simplified Procedures ◽  
Linear Matrix Equations

In this paper, a kind of complex fuzzy linear matrix equation A X ˜ B = C ˜ , in which C ˜ is a complex fuzzy matrix and A and B are crisp matrices, is investigated by using a matrix method. The complex fuzzy matrix equation is extended into a crisp system of matrix equations by means of arithmetic operations of fuzzy numbers. Two brand new and simplified procedures for solving the original fuzzy equation are proposed and the correspondingly sufficient condition for strong fuzzy solution are analysed. Some examples are calculated in detail to illustrate our proposed method.

A note on “approximate solution of dual fuzzy matrix equations”

2017 ◽  
Vol 418-419 ◽  
pp. 184-185 ◽  
Author(s):  
Jeevan Jot Kaur ◽  
Amit Kumar
Keyword(s):  
Approximate Solution ◽  
Matrix Equations ◽  
Fuzzy Matrix

scholarly journals Inconsistent LR Fuzzy Matrix Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaobin Guo ◽  
Lijuan Wu
Keyword(s):  
Approximate Solution ◽  
Matrix Equation ◽  
Generalized Inverse ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Matrix Equations ◽  
Fuzzy Matrix ◽  
Left And Right ◽  
The Mean

In this paper, the inconsistent LR fuzzy matrix equation A X ˜ = B ˜ is proposed and discussed. Firstly, the LR fuzzy matrix equation is transformed into two crisp matrix equations in which one determines the mean value and the other determines the left and right extends of fuzzy approximate solution. Secondly, the approximate solution of the LR fuzzy matrix equation is obtained by solving two crisp matrix equations according to the generalized inverse of crisp matrix theory. Then, sufficient conditions for the existence of strong LR fuzzy approximate solution are given. Finally, some numerical examples are given to illustrate our proposed method.

Research on the E-Commerce's User Experience Evaluation Model

2013 ◽  
Vol 427-429 ◽  
pp. 2859-2863
Author(s):  
Xin Xiong Liu ◽  
Qing Yun Liu ◽  
Wei Wang ◽  
Cong Mei Huang ◽  
Wen Si Li
Keyword(s):  
User Experience ◽  
Fuzzy Numbers ◽  
Evaluation Model ◽  
Comprehensive Analysis ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Matrix ◽  
Model Based ◽  
Hierarchy Model ◽  
Improved Model

Firstly, the current situations of E-commerces user experience evaluation model were analyzed. And then, fuzzy comprehensive analyses were introduced. After that, an improved E-commerces user experience evaluation model based on fuzzy comprehensive analysis was established. In improved model, user experience hierarchy model was created based on psychological-stratification, experts fuzzy evaluations of evaluation factors were integrated into fuzzy matrix by using the theory of Triangular Fuzzy Numbers. Finally an example is given to show the rationality and the effectiveness of the method.

Inverse of a fuzzy matrix of fuzzy numbers

2009 ◽  
Vol 86 (8) ◽  
pp. 1433-1452 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mehdi Ghatee ◽  
Behnam Hashemi
Keyword(s):  
Fuzzy Numbers ◽  
Fuzzy Matrix
Sign in / Sign up

Export Citation Format

Share Document