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Iranian Journal of Fuzzy Systems، جلد ۴، شماره ۲، صفحات ۳۱-۴۵
عنوان فارسی A NOTE ON THE ZIMMERMANN METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS
چکیده فارسی مقاله 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.
کلیدواژه‌های فارسی مقاله Linear programming، Fuzzy set theory، Fuzzy linear programming and fuzzy efficiency،
عنوان انگلیسی A NOTE ON THE ZIMMERMANN METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS
چکیده انگلیسی مقاله 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.
کلیدواژه‌های انگلیسی مقاله Linear programming, Fuzzy set theory, Fuzzy linear programming and fuzzy efficiency
نویسندگان مقاله محمدرضا صافی |
department of mathematices, university of shahid-bahonar kerman, kerman, iran

حمیدرضا ملکی |
department of basic sciences, shiraz university of technology, shiraz, iran
سازمان اصلی تایید شده: دانشگاه صنعتی شیراز (Shiraz university of technology)

عفت zaeimazad |
department of mathematices, university of shahid-bahonar kerman, kerman, iran

نشانی اینترنتی http://ijfs.usb.ac.ir/article_369_c50bd5faf59078df22d9c02d540aade9.pdf
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