In paper a general fuzzy matrix equation is investigated by using the embedding approach. A numerical procedure for calculating the solution is designed and a sufficient condition for the existence of fuzzy solution is derived. Two examples are given to illustrate the proposed method.
AbbasbandyS., JafarianA. and FzzatiR., Conjugate gradient method for fuzzy symmetric positive definite system of linear equations, Applied Mathematics and Computation171 (2005), 1184–1191.
2.
AbbasbandyS., EzzatiR. and JafarianA., LU decomposition method for solving fuzzy system of linear equations, Applied Mathematics and Computation172 (2006), 633–643.
3.
AbbasbandyS., OtadiM. and MoslehM., Minimal solution of general dual fuzzy linear systems, Chaos, Solitions and Fractals29 (2008), 638–652.
4.
AllahviranlooT., Numerical methods for fuzzy system of linear equations, Applied Mathematics and Computation153 (2004), 493–502.
5.
AllahviranlooT., Successive over relaxation iterative method for fuzzy system of linear equations, Applied Mathematics and Computation162 (2005), 189–196.
6.
AllahviranlooT., The adomian decomposition method for fuzzy system of linear equations, Applied Mathematics and Computation163 (2005), 553–563.
7.
AllahviranlooT., Hosseinzadeh LotfiF., Khorasani KiasariM. and KhezerlooM., On the fuzzy solution of LR fuzzy linear systems, Applied Mathematical Modelling37 (2013), 1170–1176.
8.
AllahviranlooT., MikaeilvandN. and BarkhordaryM., Fuzzy linear matrix equations, Fuzzy Optimization and Decision Making8 (2009), 165–177.
9.
AsadyB., AbbasbandyS. and AlaviM., Fuzzy general linear systems, Applied Mathematics and Computation169 (2005), 34–40.
10.
BabbarN., KumarA. and BansalA., Solving fully fuzzy linear system with arbitrary triangular fuzzy numbers, Soft Computing17 (2013), 691–702.
11.
Ben-IsraelA. and GrevilleT.N.E., Generalized inverses: Theory and applications, second edition, Springer-Verlag, New York, 2003.
12.
BermanA. and PlemmonsR.J., Nonnegative matrices in the Mathematical Sciences, Academic press, New York, 1979.
13.
DehghanM., HashemiB. and GhateeM., Solution of the full fuzzy linear systems using iterative techniques, Chaos, Solitons and Fractals34 (2007), 316–336.
14.
DehghanM. and HashemiB., Iterative solution of fuzzy linear systems, Applied Mathematics and Computation175 (2006), 645–674.
15.
DookhitramK., KanaksabeeP. and BhuruthM., Krylov subspace method for fuzzy eigenvalue problem, Journal of Intelligent and Fuzzy Systems27 (2014), 717–727.
16.
DookhitramK., LollchundR., TripathiR.K., BhuruthM. and BhuruthM., Fully fuzzy sylvester matrix equations, Journal of Intelligent and Fuzzy Systems28 (2015), 2199–2211.
17.
DuboisD. and PradeH., Operations on fuzzy numbers, Journal of Systems Science9 (1978), 613–626.
18.
FriedmanM., MaM. and KandelA., Fuzzy linear systems, Fuzzy Sets and Systems96 (1998), 201–209.
19.
GhanbariR., Solutions of fuzzy LR algebraic linear systems using linear programs, Applied Mathematical Modelling39 (2015), 5164–5173.
20.
GoetschelR. and VoxmanW., Elementary calculus, Fuzzy Sets and Systems18 (1986), 31–43.
21.
GongZ.T. and GuoX.B., Inconsistent fuzzy matrix equations and its fuzzy least squares solutions, Applied Mathematical Modelling35 (2011), 1456–1469.
22.
GongZ.T. and GuoX.B., Approximate solution of dual fuzzy matrix equations, Information Sciences266 (2014), 112–133.
23.
GuoX.B. and ShangD.Q., Fuzzy symmetric solutions of fuzzy matrix equations, Advances in Fuzzy Systems (2012), 9. Article ID 318069.
24.
GuoX.B. and ShangD.Q., Approximate solutions of LR fuzzy Sylvester matrix equations, Journal of Applied Mathematics (2013), 10. Article ID 752760.
25.
MaM., FriedmanM. and KandelA., Duality in Fuzzy linear systems, Fuzzy Sets and Systems109 (2000), 55–58.
26.
NahmiasS., Fuzzy variables, Fuzzy Sets and Systems1(2) (1978), 97–111.
27.
NuraeiR., AllahviranlooT. and GhanbariM., Finding an inner estimation of the solution set of a fuzzy linear system, Applied Mathematical Modelling37 (2013), 5148–5161.
