Solving multi-objective linear programming problems with fuzzy goals in the presence of fuzzy max-arithmetic mean relational inequality constraints

A multi-objective linear programming problem with a system of max-arithmetic mean relational inequalities as its constraints is considered. For each of the objective functions, the decision maker has a fuzzy goal. Treating each fuzzy goal, two kind of membership functions are considered: linear and hyperbolic as a nonlinear one. Then, using membership functions and Bellman-Zadeh decision, the multi-objective linear programming problem is converted to a conventional linear programming problem. Two examples are given to illustrate the procedure and compare the two different membership functions.