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

The main goal of this work is to find a better solution for a kind of multi-objective optimization problem subject to a system of fuzzy relational inequalities with max-arithmetic mean composition. First, this problem is solved and in the case that the decision maker is not satisfied with any of its solutions then, by assigning linear membership functions to the inequalties 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 find this solution easier, some simplification processes are given. After that, an algorithm is presented to generate the new solution. Finally, an example is given to illustrate the steps of the algorithm.