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Soft Computing
Published in: Soft Computing 7/2021

13-01-2021 | Methodologies and Application

An extension method for fully fuzzy Sylvester matrix equation

Authors: Liangshao Hou, Jieyong Zhou, Qixiang He

Published in: Soft Computing | Issue 7/2021

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Abstract

An extension method is proposed to solve a class of fully fuzzy Sylvester matrix equation (FFSME) under some mild assumptions. This method consists of two steps. Firstly, the fully fuzzy system is transferred into a series of interval Sylvester matrix equations through \(\alpha \)-cut. Secondly, these interval systems are extended into crisp systems which is easy to be solved. The solutions of FFSME are not presumed to be triangular-type fuzzy numbers. Moreover, some examples are presented to show the validity of our method.
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Literature
Antoulas AC (2005) Approximation of large-scale dynamical systems. SIAM, Philadelphia, PACrossRef
Babbar N, Kumar A, Bansal A (2013) Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers \((m,\alpha, \beta )\). Soft Comput 17(4):691–702CrossRef
Bartels RH, Stewart GW (1972) Solution of the matrix equation AX +XB = C. Commun ACM 15(9):820–826CrossRef
Basaran MA (2012) Calculating fuzzy inverse matrix using fuzzy linear equation system. Appl Soft Comput 12(6):1810–1813CrossRef
Bouhamidi A, Jbilou K (2007) Sylvester Tikhonov-regularization methods in image restoration. J Comput Appl Math 206(1):86–98MathSciNetCrossRef
Buckley JJ, Eslami E, Feuring T (2002) Fuzzy mathematics in economics and engineering. Springer, BerlinCrossRef
Dookhitram K, Lollchund R, Tripathi RK, Bhuruth M (2015) Fully fuzzy Sylvester matrix equation. J Intell Fuzzy Syst 28(5):2199–2211MathSciNetMATH
Dubois DJ (1980) Fuzzy sets and systems: theory and applications, vol 144. Academic Press, CambridgeMATH
Fernando KV, Nicholson H (1983) On the structure of balanced and other principal representations of SISO systems. IEEE Trans Automat Contr 28(2):228–231MathSciNetCrossRef
Fortin J, Dubois D, Fargier H (2008) Gradual numbers and their application to fuzzy interval analysis. IEEE Trans Fuzzy Syst 16(2):388–402CrossRef
Ghanbari R, Mahdavi-Amiri N (2015) Fuzzy LR linear systems: quadratic and least square models to characterize exact solutions and an algorithm to compute approximate solutions. Soft Comput 19(1):205–216CrossRef
Golub G, Nash S, Van Loan CF (1979) A Hessenberg–Schur method for the problem AX +XB = C. IEEE Trans Automat Control 24(6):909–913MathSciNetCrossRef
Guo X, Shang D (2013) Approximate solution of LR fuzzy Sylvester matrix equations. J Appl Math 1–10:2013MathSciNetMATH
Hammarling SJ (1982) Numerical solution of the stable, non-negative definite Lyapunov equation. IMA J Numer Anal 2(3):303–323
He Q, Hou L, Zhou J (2017) The solution of fuzzy Sylvester matrix equation. Soft Comput pp 1–9
Hyland DC, Bernstein DS (1984) The optimal projection equations for fixed-order dynamic compensation. IEEE Trans Automat Contrib 29(11):1034–1037MathSciNetCrossRef
Jones A, Kaufmann A, Zimmermann HJ (2012) Fuzzy sets theory and applications, vol 177. Springer, Berlin
Kressner D (2008) Block variants of Hammarling’s method for solving Lyapunov equations. ACM Trans Math Softw 34(1):1MathSciNetCrossRef
Liu HK (2010) On the solution of fully fuzzy linear systems. Int J Comput Math Sci 4(1):29–33MathSciNet
Lu A, Wachspress EL (1991) Solution of Lyapunov equations by alternating direction implicit iteration. Comput Math Appl 21(9):43–58MathSciNetCrossRef
Raich VV, Triphath, RK, Bawa, NPS, Dookhitram, K, Dayal, SK (2011) Application of interval valued fuzzy matrices in medical diagnosis via a new approach. In: 2011 International Conference on Multimedia Technology, pp 3440–3443. IEEE
Salkuyeh DK (2011) On the solution of the fuzzy Sylvester matrix equation. Soft Comput 15(5):953–961CrossRef
Smith RA (1968) Matrix equation \({X}{A} + {B}{X} = {C}\). SIAM J Appl Math 16(1):198–201
Sorensen DC, Zhou Y (2003) Direct methods for matrix Sylvester and Lyapunov equations. J Appl Math Comput 2003(6):277–303MathSciNetMATH
Triphathi RK, Raich VV, Dookhitra K, Dayal SK, Hareesh AS (2012) Similarity between max min and riv technique with reference to two diseases diarrhea and diabetes. In: National Conference on Computational Intelligence and Signal Processing, pp 170–174
Metadata
Title
An extension method for fully fuzzy Sylvester matrix equation
Authors
Liangshao Hou
Jieyong Zhou
Qixiang He
Publication date
13-01-2021
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 7/2021
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-021-05573-z

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