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 methodsproposed by Zimmermann, Verdegay, Chanas and Werners are used more often thanthe others. In the Zimmerman method (ZM) the main objective function cx is addedto 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 optimalsolutions (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 theAOS have the same λ , they have the same values for the new LP. Therefore, unlesswe check the value of cx for all AOS, it may be that we do not present the bestsolution to the decision maker (DM); it is possible that cx is unbounded but ZMpresents a bounded solution as the optimal solution. In this note, we propose analgorithm for eliminating these difficulties.

کلیدواژه ها:

Linear programming ، Fuzzy set theory ، Fuzzy linear programming and fuzzy efficiency