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

Abstract

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.

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

“…Accordingly, Relation (1) and its solutions have a signi cant role in solving Relation (2). Correspondingly, in the following, some previously obtained results are stated [4,5,11,12] Nevertheless, generally, when the objective functions con ict with each other, such a complete optimal solution which concurrently minimizes all of the objective functions does not always exist. Therefore, Pareto optimal solution is used as a substitute [12].…”

“…Also, it can be solved by heuristic methods such as the Genetic algorithm [15]. If the problem has several solutions and the DM is satis ed with none of them, then the DM shall choose one of these solutions based on his/her point of view in order to obtain one fuzzy solution [11]. Now, using the selected solution of Relation (1), we try to solve Relation (2).…”

“…In [1], a multiobjective optimization problem in the presence of a system of FREs with max-arithmetic mean composition has been considered. In [11], the authors have studied the same problem with FRIs.…”

“…In Section 2, a multi-objective optimization of linear functions with ordinary inequalities in the presence of a max-arithmetic mean composition problem is studied [11]. Then, using a selected solution and linear membership functions, the multi-objective optimization problem in the presence of the fuzzy inequalities is converted into another problem with one objective function.…”