Title: A modification on 'ranking DMUs by L₁-norm' and introducing a novel ranking method by Tchebycheff norm with fuzzy data in DEA

Authors: Babooshka Shavazipour; Hamed Zhiani Rezai; Alireza Davoodi

Addresses: Department of Statistical Sciences, Faculty of Science, University of Cape Town, Rondebosch 7701, Cape Town, South Africa ' Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran ' Young Researchers and Elite Club, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran

Abstract: Jahanshahloo et al. (2009) proposed a ranking model to efficient decision-making units (DMUs) including fuzzy data. The aforementioned method is based on L₁-norm measure combined with the weighted signed distance between two fuzzy numbers. Firstly, it is shown by an example that the proposed method may not work correctly. And then, the modification of the method is presented in this paper. What is more, for more extension, another approach is introduced to ranking extremely efficient decision-making units in data envelopment analysis (DEA) models with fuzzy data. This approach is based on the Tchebycheff norm (infinity norm). Then, it is shown that this new model can address some shortcoming of the L₁-norm proposed by previous authors. Finally, to demonstrate the concept, the case of 30 branches of social welfare bureau in Tehran is revisited and solutions are compared.

Keywords: data envelopment analysis; DEA; DMU ranking; fuzzy data; efficiency; decision-making units; DMUs; Tchebycheff norm; fuzzy logic; social welfare bureaux; Iran.

DOI: 10.1504/IJOR.2017.082619

International Journal of Operational Research, 2017 Vol.28 No.4, pp.528 - 550

Received: 21 Nov 2014
Accepted: 28 Jan 2015
Published online: 03 Mar 2017 *

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