A NOTE ON THE 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 the Zimmerman method (ZM) the main objective function cx is added to the constraints as a fuzzy goal and the corresponding linear programming (LP) problem with a new objective ) (λ is solved. When this new LP has alternative optimal solutions (AOS), ZM may not always present the "best" solution. Two cases may occur: cx may have different bounded values for the AOS or be unbounded. Since all of the AOS have the same λ , they have the same values for the new LP. Therefore, unless we check the value of cx for all AOS, it may be that we do not present the best solution to the decision maker (DM); it is possible that cx is unbounded but ZM presents a bounded solution as the optimal solution. In this note, we propose an algorithm for eliminating these difficulties.