Solving Generalized DEA/AR Model With Fuzzy Data and Its Application to Evaluate the Performance of Manufacturing Enterprises

Document Type : Research Paper


1 Department of Management, Humanities College, Hazrat-e Masoumeh University, Qom, Iran

2 Department of Mathematics, University of Qom, Qom, Iran


The use of conventional data envelopment analysis (DEA) models in real-world problems are limited because of some restrictions that must be considered in the model such as imprecise or vague data in inputs and outputs as well as additional information or assumptions. One way to handle this problem is by using fuzzy DEA with assurance regions (FDEA/AR) models. There is a common approach in almost all the suggested methods for solving FDEA/AR models. However, in this paper, we show that in some DEA/AR models, applying this approach can be led to inappropriate results. Four theorems are given to provide some sufficient conditions for a DMU to be the DEA/AR efficient. These theorems can be used to check the accuracy of the presented methods for solving FDEA/AR models, too. Moreover, a new method for solving a generalized FDEA/AR model that includes established DEA models such as CCR model (Charnes et al., 1978), BCC model (Banker et al., 1984), FG model (Färe & Grosskopf, 1985), and ST model (Seiford & Thrall, 1990) is proposed. These models are constant, variable, non-decreasing, and non-increasing returns to scale models, respectively. The proposed method is applied to evaluate the performance of manufacturing enterprises.


Main Subjects

Article Title [Persian]

حل مدل DEA / AR تعمیم یافته با داده های فازی و کاربرد آن در ارزیابی عملکرد شرکت های تولیدی

Authors [Persian]

  • روح اله عباسی شورشجانی 1
  • علی اصغر فروغی 2
1 دانشکده علوم انسانی ، دانشگاه حضرت معصومه (س)، قم، ایران
2 دانشکده ریاضی ، دانشگاه قم، قم، ایران
Abstract [Persian]

استفاده از مدلهای تحلیل پوششی داده های متعارف برای مسائل دنیای واقعی به دلیل برخی محدودیت هایی که لازم است در مدل رعایت شود مانند وجود داده های نادقیق یا مبهم در ورودیها و خروجی ها و همین طور وجود اطلاعات یا فرضیات اضافی، با محدودیت همراه است. یکی از راههای حل این مشکل، استفاده از مدلهای تحلیل پوششی داده های فازی با نواحی محدود (FDEA/AR) است. تقریباً یک رویکرد مشترک در تمام روشهای پیشنهادی برای حل مدلهای FDEA/AR وجود دارد. با این حال، در این مقاله نشان می دهیم که در برخی از مدلهای  DEA/AR استفاده از این رویکرد می تواند منجر به نتایج نامناسب شود. چهار قضیه ارائه شده است تا برخی شرایط کافی برای کارای DEA/AR بودن یک واحد تصمیم را فراهم نماید. از این قضایا می توان برای بررسی صحت روشهای ارائه شده برای حل مدلهای FDEA/AR نیز استفاده نمود. علاوه بر این، یک روش جدید برای حل یک مدل FDEA/AR تعمیم یافته ارائه شده که شامل مدلهای مشهور DEA مانند CCR، BCC، FG، و ST است. این مدلها به ترتیب با بازده به مقیاس ثابت، متغیر، غیر کاهشی، و غیر افزایشی می باشند. روش ارائه شده برای ارزیابی عملکرد شرکت های تولیدی استفاده شده است.

Keywords [Persian]

  • تحلیل پوششی داده ها
  • تحلیل پوششی داده های فازی
  • نواحی محدود
  • اعداد فازی
  • کارایی
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