A NOTE ON THE ZIMMERMANN METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS

Document Type : Research Paper

Authors

1 DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN, KERMAN, IRAN

2 DEPARTMENT OF BASIC SCIENCES, SHIRAZ UNIVERSITY OF TECHNOLOGY, SHIRAZ, IRAN

Abstract

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.

Keywords

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Iranian Journal of Fuzzy Systems
Volume 4, Issue 2 - Serial Number 2
September and October 2007
Pages 31-45

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