Solving Fuzzy Multiobjective Linear Programming Problems Using Embedding Theorem

Fuzzy multiobjective linear programming problems are solved in this paper by considering the concepts of the minimizer and ideal minimizer. A useful embedding theorem is provided to define the partial orderings among the space of fuzzy intervals in R, where the partial orderings are generated by some convex cones. Using the partial orderings, we can propose the concept of minimal elements such that the concepts of the minimizer and ideal minimizer of fuzzy multiobjective linear programming problems can be proposed. The main issue is to separately derive the optimality conditions for the minimizer and ideal minimizer. Finally, we consider some practical problems by providing a specific convex cone such that the minimizer and ideal minimizer can be obtained by solving the conventional linear programming problems using the simplex method.