Another modification from two papers of Ghodousian and Khorram and Khorram et al.

In this paper, we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max-min and the max-average composition and the max-star composition, respectively. They have been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, Solving a linear programming problem with the convex combination of the max-min and the max-average fuzzy relation equations, Appl. Math. Comput. 180 (2006) 411-418] and Khorram et al. [E. Khorram, A. Ghodousian, A. Abbasi Molai, Solving linear optimization problems with max-star composition equation constraints, Appl. Math. Comput. 179 (2006) 654-661], respectively. Firstly, we show that the “Tabular method algorithm” in the first paper and the “First procedure” in the second paper may not lead to the optimal solutions of the two models in some cases. Secondly, we generalize the proposed algorithm by Abbasi Molai and Khorram [A. Abbasi Molai, E. Khorram, A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian, Appl. Math. Comput. 190 (2007) 1161-1167] to solve the two models. In fact, it modifies the presented algorithms in the two papers. Finally, some numerical examples are given to illustrate the purposes.