This paper shows that the exact solutions for fully fuzzy linear systems for all examples in [1] are nonfuzzy solutions, and that the proposed solutions in [1] do not correspond to these systems. In addition, approximate fuzzy solutions are provided for all the examples. Finally, this paper shows the efficiency of the provided solutions by using the distance metric function introduced in [13].
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Abbasbandy and M. S. Hashemi, “Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm,” Comput. Math. Model, 23, 107–123 (2012).
T. Allahviranloo, E. Haghi, and M. Ghanbari, “The nearest symmetric fuzzy solution for a symmetric fuzzy linear system,” An. St. Univ. Ovidius Constanta, 20, 151–172 ( 2012).
M. Dehghan, B. Hashemi, and M. Ghatee, “Computational methods for solving fully fuzzy linear systems,” Appl. Math. Comput., 179, 328–343 (2006).
M. Dehghan, B. Hashemi, and M. Ghatee, “Solution of the fully fuzzy linear systems using iterative techniques,” Chaos, Solitons Fractals, 34, 316–336 (2007).
D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York (1980).
R. Ezzati, S. Khezerloo, and A. Yousefzadeh, “Solving Fully Fuzzy Linear System of Equations in General Form,” J. Fuzzy Set Valued Anal., 2012, 1–11 (2012).
M. Friedman, M. Ming, and A. Kandel, “Fuzzy linear systems,” Fuzzy Sets Syst., 96, 201–209 (1998).
G. Malkawi, N. Ahmad, and H. Ibrahim, “Revisiting Fuzzy Approach for Solving System of Linear Equations,” ICDeM 2012, 13 – 16 March, Kedah, Malaysia, 157–164 (2012).
G. Malkawi, N. Ahmad, and H. Ibrahim, “Solving Fully Fuzzy Linear System with the Necessary and Sufficient Condition to have a Positive Solution,” Appl. Math, 8, No. 3, 1003–1019 (2014).
G. Malkawi, N. Ahmad, and H. Ibrahim, Row Reduced Echelon Form for Solving Fully Fuzzy System with Unknown Coefficients. Journal of Fuzzy Set Valued Analysis, 2014, 1–18, (2014).
G. Malkawi, N. Ahmad, and H. Ibrahim, On the weakness of linear programming to interpret the nature of solution of fully fuzzy linear system,” J. Uncertainty Anal. Appl., 2, No. 1, 1–23 (2014).
G. Malkawi, N. Ahmad, and H. Ibrahim, “A note on the nearest symmetric fuzzy solution for a symmetric fuzzy linear system,” An. St. Univ. Ovidius Constanta, 2014. (Accepted for Publication).
M. Ming, M. Friedman, and A. Kandel, “General fuzzy least squares ,” Fuzzy Sets and Systems, 88, 107–118 (1997).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Malkawi, G., Ahmad, N., Ibrahim, H. et al. A Note on “Solving Fully Fuzzy Linear Systems by Using Implicit Gauss–Cholesky Algorithm”. Comput Math Model 26, 585–592 (2015). https://doi.org/10.1007/s10598-015-9295-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-015-9295-9