Linear fractional multi-objective optimization problems subject to fuzzy relational equations with a continuous Archimedean triangular norm

In this paper, linear fractional multi-objective optimization problems subject to a system of fuzzy relational equations (FREs) using the max-Archimedean triangular norm composition are considered. First, some theorems and results are presented to simplify systems of fuzzy relational equations. Next, the feasible set of the optimization problem is reduced. Then, the linear fractional multi-objective optimization problem is converted to a linear one using Nykowski and Zolkiewski’s approach. Furthermore, the efficient solutions are obtained by applying the improved εε-constraint method.In addition, we design an algorithm to generate consistent systems of fuzzy relational equations, randomly, using the covering problem. Finally, the proposed method is effectively tested by solving a randomly generated consistent test problem.