Soft Computing

, Volume 22, Issue 7, pp 2095–2103 | Cite as

A method for solving fuzzy matrix equations

  • M. Amirfakhrian
  • M. Fallah
  • R. Rodríguez-López


There are many reported studies, in which researchers tried to solve a system of fuzzy linear equations numerically. In this paper, a numerical method for solving fuzzy system \(A{\tilde{X}} B={\tilde{C}}\) of matrix equations is investigated. As it can be observed in the form of these equations, the unknown matrix X, which is the solution to these equations, has a left-hand coefficient matrix A and a right-hand coefficient matrix B. Such character makes these equations different from other equations in the form of \(A{\tilde{X}}={\tilde{B}}\). In the aforesaid equations, A and B are crisp matrices and \({\tilde{C}}\) and \({\tilde{X}}\) are matrices with fuzzy arrays. In this work using the parametric form of fuzzy linear equations and presenting an algorithm, two systems of equations will be developed and solved afterward. A comparison of the number of multiplications in this method with a different one will be drawn afterward. Some numerical examples are given to illustrate the effectiveness of the proposed method.


Fuzzy number Fuzzy system Fuzzy linear equations 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Central Tehran BranchIslamic Azad UniversityTehranIran
  2. 2.Facultade de MatemáticasCampus Universitario SurSantiago de CompostelaSpain

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