Abstract An optimization problem of a linear objective function subject to a system of fuzzy relational inequalities based on max-average composition and fuzzy inequality is presented. This problem is converted to a new one with ordinary inequalities by using linear membership functions and Bellman-Zadeh decision. Then, dimension of the last problem is reduced and an algorithm is presented to generate the optimal solution of the initial optimization problem. Two numerical examples are given to illustrate the steps of the algorithm. Some aspects of sensitivity analysis of the problem is investigated.