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.

scholarly journals Common Fixed-Point Results in Ordered Left (Right) Quasi- b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Hemant Kumar Nashine ◽  
Sourav Shil ◽  
Hiranmoy Garai ◽  
Lakshmi Kanta Dey ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Ordered Sets ◽  
Nonlinear Matrix ◽  
Fractional Differential ◽  
Left And Right

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

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 Conjugate gradient algorithm for consistent generalized Sylvester-transpose matrix equations

2022 ◽  
Vol 7 (4) ◽  
pp. 5386-5407
Author(s):  
Kanjanaporn Tansri ◽  
◽  
Sarawanee Choomklang ◽  
Pattrawut Chansangiam
Keyword(s):  
Approximate Solution ◽  
Conjugate Gradient ◽  
Matrix Equation ◽  
Numerical Experiments ◽  
Finite Sequence ◽  
Gradient Algorithm ◽  
Matrix Equations ◽  
Effective Algorithm ◽  
Initial Matrix ◽  
And Performance

<abstract><p>We develop an effective algorithm to find a well-approximate solution of a generalized Sylvester-transpose matrix equation where all coefficient matrices and an unknown matrix are rectangular. The algorithm aims to construct a finite sequence of approximated solutions from any given initial matrix. It turns out that the associated residual matrices are orthogonal, and thus, the desire solution comes out in the final step with a satisfactory error. We provide numerical experiments to show the capability and performance of the algorithm.</p></abstract>

scholarly journals A Study on Measurements of Different Dimensions of Maxillary Sinus by Computed Tomography in Adult Nepalese Population

2018 ◽  
Vol 8 (2) ◽  
pp. 8-12
Author(s):  
Umesh Prasad Khanal ◽  
Anupama Adhikari ◽  
Mukunda Prasad Humagain
Keyword(s):  
Computed Tomography ◽  
Maxillary Sinus ◽  
Anterior Wall ◽  
Mean Value ◽  
Forensic Sciences ◽  
P Value ◽  
Male Population ◽  
Different Dimensions ◽  
Left And Right ◽  
The Mean

Introduction: Measurement of different dimensions of maxillary sinus and anterior wallthickness of maxillary sinus by Computed Tomography in normal Nepalese populationMethods: Dimensions of 90 patients were measured in CT PNS using Syngovia Software. AP diameter, width and anterior wall thickness were measured in axial images and height was measured in coronal images.Results: The mean volume of maxillary sinuses in study of male population on left and right side were 17.09 cm3±3.89, 17.19 cm3 ±4 respectively whereas in female were 15.64 cm3±3.5 and 15.21cm3±3.2 respectively as shown in Table 1. This shows the volume of male was significantly larger than female with P- Value = 0.012 (<0.05). Similarly, the thickness of Anterior Wall (AW) of maxillary sinus was also measured in this study and the mean value of left and right side in male were 0.16cm± 0.04 and 0.15cm± 0.03 respectively and in female were 0.12cm± 0.04 and 0.14cm± 0.02 respectively.Conclusion: This study showed that CT is a reliable method for the measurement of different dimensions of the maxillary sinus. The result showed greater mean value of volume in male than female with significant differences. So this study concluded that the measurement of volume of maxillary sinus can help in the identification of gender which can be very useful for forensic sciences.

scholarly journals Curves with zero derivative in F-spaces

1981 ◽  
Vol 22 (1) ◽  
pp. 19-29 ◽  
Author(s):  
N. J. Kalton
Keyword(s):  
Characteristic Function ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Continuous Map ◽  
Left And Right ◽  
The Mean ◽  
Image Position ◽  
Locally Convex

Let X be an F-space (complete metric linear space) and suppose g:[0, 1] → X is a continuous map. Suppose that g has zero derivative on [0, 1], i.e.for 0≤t≤1 (we take the left and right derivatives at the end points). Then, if X is locally convex or even if it merely possesses a separating family of continuous linear functionals, we can conclude that g is constant by using the Mean Value Theorem. If however X* = {0} then it may happen that g is not constant; for example, let X = Lp(0, 1) (0≤p≤1) and g(t) = l[0,t] (0≤t≤1) (the characteristic function of [0, t]). This example is due to Rolewicz [6], [7; p. 116].

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 MEAN VALUE TYPE INEQUALITIES FOR QUASINEARLY SUBHARMONIC FUNCTIONS

2013 ◽  
Vol 55 (2) ◽  
pp. 349-368 ◽  
Author(s):  
OLEKSIY DOVGOSHEY ◽  
JUHANI RIIHENTAUS
Keyword(s):  
Sufficient Conditions ◽  
Continuous Functions ◽  
Mean Value ◽  
Necessary And Sufficient Conditions ◽  
Subharmonic Functions ◽  
Mean Value Inequality ◽  
The Mean ◽  
Mean Value Inequalities ◽  
Necessary And Sufficient ◽  
Bounded Sets

AbstractThe mean value inequality is characteristic for upper semi-continuous functions to be subharmonic. Quasinearly subharmonic functions generalise subharmonic functions. We find the necessary and sufficient conditions under which subsets of balls are big enough for the characterisation of non-negative, quasinearly subharmonic functions by mean value inequalities. Similar result is obtained also for generalised mean value inequalities where, instead of balls, we consider arbitrary bounded sets, which have non-void interiors and instead of the volume of ball some functions depending on the radius of this ball.

scholarly journals Arbitrary Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equation

2021 ◽  
Author(s):  
Ahmed Elsayed ◽  
Nazihah Ahmad ◽  
Ghassan Malkawi
Keyword(s):  
Matrix Equation ◽  
Linear Equations ◽  
Matrix Equations ◽  
Sylvester Matrix Equation ◽  
Fuzzy Matrix ◽  
Sylvester Matrix ◽  
Multiplication Operation ◽  
Non Linear ◽  
The Stability ◽  
Non Linear System

Abstract There are many applications where couple of Sylvester matrix equations (CSME) are required to be solved simultaneously, especially in analyzing the stability of control systems. However, there are some situations in which the crisp CSME are not well equipped to deal with the uncertainty problem during the process of stability analysis in control system engineering. Thus, in this paper a new method for solving a coupled trapezoidal fully fuzzy Sylvester matrix equation (CTrFFSME) with arbitrary coefficients is proposed. The arithmetic fuzzy multiplication operation is applied to convert the CTrFFSME into a system of non-linear equations. Then the obtained non-linear system is reduced and converted to a system of absolute equations where the fuzzy solution is obtained by solving that system. The proposed method can solve many unrestricted fuzzy systems such as Sylvester and Lyapunov fully fuzzy matrix equations with triangular and trapezoidal fuzzy numbers. We illustrate the proposed methods by solving numerical example.

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.

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