An overall profit Malmquist productivity index with fuzzy and interval data

Ali Emrouznejad, Mohsen Rostamy-Malkhalifeh, Adel Hatami-Marbini, Madjid Tavana, Nazila Aghayi

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)


Although crisp data are fundamentally indispensable for determining the profit Malmquist productivity index (MPI), the observed values in real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized with fuzzy and interval methods. In this paper, we reformulate the conventional profit MPI problem as an imprecise data envelopment analysis (DEA) problem, and propose two novel methods for measuring the overall profit MPI when the inputs, outputs, and price vectors are fuzzy or vary in intervals. We develop a fuzzy version of the conventional MPI model by using a ranking method, and solve the model with a commercial off-the-shelf DEA software package. In addition, we define an interval for the overall profit MPI of each decision-making unit (DMU) and divide the DMUs into six groups according to the intervals obtained for their overall profit efficiency and MPIs. We also present two numerical examples to demonstrate the applicability of the two proposed models and exhibit the efficacy of the procedures and algorithms.

Original languageEnglish
Pages (from-to)2827-2838
Number of pages12
JournalMathematical and Computer Modelling
Issue number11-12
Early online date21 Jul 2011
Publication statusPublished - 1 Dec 2011
Externally publishedYes


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