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
2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang

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.


2014 ◽  
Vol 266 ◽  
pp. 112-133 ◽  
Author(s):  
Zengtai Gong ◽  
Xiaobin Guo ◽  
Kun Liu

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang

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.


2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yirong Sun ◽  
Junyang An ◽  
Xiaobin Guo

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.


2017 ◽  
Vol 418-419 ◽  
pp. 184-185 ◽  
Author(s):  
Jeevan Jot Kaur ◽  
Amit Kumar

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaobin Guo ◽  
Lijuan Wu

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.


2013 ◽  
Vol 427-429 ◽  
pp. 2859-2863
Author(s):  
Xin Xiong Liu ◽  
Qing Yun Liu ◽  
Wei Wang ◽  
Cong Mei Huang ◽  
Wen Si Li

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.


2009 ◽  
Vol 86 (8) ◽  
pp. 1433-1452 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mehdi Ghatee ◽  
Behnam Hashemi
Keyword(s):  

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