نوع مقاله : مقاله پژوهشی - کاربردی

نویسندگان

گروه ریاضی، دانشگاه پیام نور، تهران، ایران.

چکیده

مدل تحلیل پوششی داده‌ها مبتنی بر برنامه‌ریزی آرمانی (GDEA) با افزایش میزان تفکیک‌پذیری و ارائه وزن‌های واقعی به واحدهای تصمیم‌گیری (DMU) به دنبال رفع نواقص مدل تحلیل پوششی داده‌ها (DEA) کلاسیک و پایه‌ای می‌باشد. نتایج تجربی حاکی از عدم رفع کامل نقایص در برخی از نمونه‌های مورد آزمایش توسط مدل‌های GDEA می‌باشند.همچنین در محاسبه جواب بهینه با روش‌های مختلف ارزیابی کارایی واحدها، با دسته‌ای از جواب‌های بهینه پارتو مواجه هستیم که یک مدیر تصمیم‌گیرنده را در انتخاب مناسب‌ترین جواب با چالش جدی مواجه می‌کند. برای رفع این معضل، در گام نخست در این مقاله، با استفاده از مفاهیم منطق فازی، رویکرد F-GDEA را که یک مدل مبتنی بر منطق فازی در حل مدل‌های GDEA است، پیشنهاد می‌دهیم که باعث افزایش قدرت تفکیک‌پذیری روش‌ها در رتبه‌بندی واحدها می‌شود. در گام دوم، با در نظر گرفتن رتبه‌بندی‌های متنوع حاصل از اعمال مدل‌های برنامه‌ریزی مختلف، با استفاده از رویکرد F-GDEA یک رویکرد تلفیقی فازی جدید به نام اختصاری HF-GDEA پیشنهاد می‌دهیم. با این رویکرد پیشنهادی، رتبه‌‌بندی حاصل از روش‌های مختلف را با یکدیگر تلفیق نموده و یک‌ رتبه‌بندی جدید برای واحدهای تصمیم‌گیری ارائه می‌دهیم، به‌عبارت‌دیگر، رویکرد HF-GDEA، امکان مقایسه و درنتیجه انتخاب یک جواب بهینه از بین جواب‌های بهینه پارتو را فراهم می‌سازد. در پایان رویکرد پیشنهادی بر روی دو نمونه کاربردی اعمال و نتایج عددی آن آورده شده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

HF-GDEA: hybrid fuzzy approach to Integrate ranking of goal models in DEA

نویسندگان [English]

  • Ham,id Reza Yoosefzade
  • Azam Teimuri
  • Aghile Heidari

Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.

چکیده [English]

The models of Data Envelopment Analysis (DEA) based on Goal Programming (GDEA) seeks to address some drawbacks of classical DEA by increasing the degree of resolution and providing real weights to Decision-Making Units (DMUs). Experimental results indicate that the GDEA models do not completely cope with these in some cases which are tested. Also, in calculating the optimal solution with different methods of evaluating the efficiency of units, we are faced with a group of Pareto optimal solutions that make a decision maker facing a serious challenge in choosing the most appropriate solution. To solve this, in the first step, this paper uses the concepts of fuzzy logic and then proposes the F-GDEA approach based on fuzzy logic in solving the GDEA models, which increases the resolution of the methods to rank the units. In the second step, by using the F-GDEA approach, we propose a new hybridized fuzzy approach called HF-GDEA for short, taking into account the various ranking results from the different programming models. With this new proposed approach, we combine the rankings obtained from different methods and present a new ranking for the DMUs. In other words, the HF-GDEA approach makes it possible to compare and thus select an optimal solution from Pareto's optimal solutions set. Finally, the proposed approach is applied to two practical examples and their numerical results are presented.

کلیدواژه‌ها [English]

  • Goal programming
  • Multi-objective optimization
  • Data envelopment analysis (DEA)
  • Fuzzy logic
  • Pareto solutions
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