An overall profit Malmquist productivity index with fuzzy and interval data
(2011) Mathematical and Computer Modelling — Vol. 54, n° 11-12, p. 2827-2838 (2011)
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- Authors
- Abstract
- 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 interval 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.
- Affiliations
Aston University Aston Business School Islamic Azad University Department of Mathematics, Science and Research Brach" La Salle University Management Information Systems, Lindback Distinguished Chair of Information Systems" Islamic Azad University Department of Mathematics, Science and Research Branch
Citations
Emrouznejad, A., Rostamy-Malkhalifeh, M., Hatami-Marbini, A., Tavana, M., & Aghayi, N. (2011). An overall profit Malmquist productivity index with fuzzy and interval data. Mathematical and Computer Modelling, 54(11-12), 2827-2838. https://doi.org/10.1016/j.mcm.2011.07.003 (Original work published 2011)