Soft Computing

, Volume 22, Issue 7, pp 2095–2103

# A method for solving fuzzy matrix equations

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

## 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.

## Keywords

Fuzzy number Fuzzy system Fuzzy linear equations

## Notes

### Conflict of interest

The authors declare that they have no conflict of interest.

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