A Note on Zimmermann Method for Solving Fuzzy Linear Programming problems

There are several methods for solving fuzzy linear programming (FLP) problems. When the constraints and/or the objective function are fuzzy, the methods proposed by Zimmermann, Verdegay, Chanas and Werners are used more often than the others. In this note, we investigate Zimmerman method (ZM). In this method, the main objective function is added to the constraints as a fuzzy goal and the corresponding linear programming (LP) problem with a new objective () is solved. When the corresponding LP has alternative optimal solutions (AOS), this method may not always present the "best" solution. Two cases may occur: may have different bounded values for AOS or be unbounded. Since all of the AOS have the same, they have the same values for corresponding LP. Therefore, unless we check the value of for all AOS, it may be that we do not present the best solution to the decision maker (DM); it is possible that is unbounded but ZM presents a bounded solution as the optimal solution. In this note, we propose an algorithm for eliminating these difficulties.