Fuzzy multi-objective optimization of linear functions subject to max-arithmetic mean relational inequality constraints

The main goal of this work is to nd a better solution to a kind of multiobjective optimization problem subject to a system of fuzzy relational inequalities with max-arithmetic mean composition. first, this problem is solved and, then, in the case that the decision maker is not satis ed with any of the solutions, by assigning linear membership functions to the inequalities in the constraints and objective functions and using bellman- zadeh decision, a new solution is found. this new solution does not belong to the feasible domain but is considered acceptable based on the decision maker's view. in order to nd this solution easier, some simpli cation processes are given. afterwards, an algorithm is presented to generate the new solution. finally, an example is given to illustrate the steps of the algorithm.