Optimization of fuzzy relational equations with a linear convex combination of max-min and max-average compositions

Max-min and max-product compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations. Both are members in the class of maxt-norm composition. In this study, a linear convex combination of max-min and max-average compositions is considered for the same optimization model, which does not belong to the max-tnorm composition. However, this convex combined composition generates some properties of the solution set that are similar to the max-product composition, but different with max-min composition. Hence, the method applied to optimize the linear programming problem with max-product composition can be employed again to solve the same problem. Moreover, this study will show that the tabular method provided by Ghodousian and Khorram can not guarantee to obtain an optimal solution for the same optimization model.