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A method for solving fuzzy matrix equations

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    M. Amirfakhrian & M. Fallah

  2. Facultade de Matemáticas, Campus Universitario Sur, 15782, Santiago de Compostela, Spain

    R. Rodríguez-López

Authors
  1. M. Amirfakhrian
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  2. M. Fallah
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  3. R. Rodríguez-López
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Correspondence to M. Amirfakhrian.

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The authors declare that they have no conflict of interest.

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Communicated by A. Di Nola.

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Amirfakhrian, M., Fallah, M. & Rodríguez-López, R. A method for solving fuzzy matrix equations. Soft Comput 22, 2095–2103 (2018). https://doi.org/10.1007/s00500-017-2680-x

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