Reduction of DEA-Performance Factors Using Rough Set Theory: An Application of Companies in the Iranian Stock Exchange

Document Type : Research Paper


Department of Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran



he financial management field has witnessed significant developments in recent
years to help decision makers, managers and investors, to made optimal decisions.
In this regard, the institutions investment strategies and their evaluation methods
continuously change with the rapid transfer of information and access to the fi-
nancial data. When information is available as several inputs and output factors,
the data envelopment analysis (DEA) applies to calculate the efficiency of com-
panies. Distinguishing efficient companies from inefficient ones, makes it possi-
ble for the financial managers to select suitable portfolios. The discriminating
power of DEA depends on the number of companies under evaluation and the
number of inputs and outputs. When the number of inputs and outputs are high
compared to the number of units, most of the units will be evaluated as efficient,
thus the discriminating power of DEA decreases and the results are not reliable.
To deal with this problem, the Quick-Reduct algorithm of the rough set theory
(RST) was used in this study to reduce inputs or outputs. It should be noted that
the advantage of this algorithm is its ability to use negative data.


Main Subjects

[1]                Cooper, W.W., Seiford, L.M., and Tone, K., Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software, 2nd ed., Springer, Berlin, 2007. Doi: 10.1007/978-0-387-45283-8.
[2]                Bowlin, W.F., Measuring Performance: An Introduction to Data Envelopment Analysis(DEA), The Journal of Cost Analysis, 1998, 15(2), P. 3-27. Doi: 10.1080/08823871.1998.10462318.
[3]                 Raab, R., and Lichty, R., Identifying sub-areas that comprise a greater metropolitan area: the criterion of country relative efficiency. Journal of Regional Science, 2002, 42(3),579–594. Doi:10.1016/j.ijpe .2011.11.010.
[4]                Angulo-Meza, L., and Lins, M., Review of Methods for Increasing Discrimination in Data Envelopment Analysis, Annals of Operations Research, 2002, 116(1-4), P. 225–242. Doi:10.1023/A:1021340 616758.
[5]                Podinovski, V., and Thanassoulis, E., Improving discrimination in data envelopment analysis: some practical suggestions, Journal of Productivity Analysis, 2007, 28(1-2), P.117–126. Doi: 10.1007/s11123-007-0042-x.
[6]                Andersen, P., and Pitersen, N.C., A Procedure for Ranking Efficient Units in Data Envelopment Analysis, Management Science, 1993, 39(10), P. 1261-1264. Doi: 10.1287/mnsc.39.10.1261.
[7]                Sexton, T. R., The Methodology of Data Envelupment Analysis, New Directions for Program Evaluation, 1986, 32, P. 7-29. Doi: 10.1002/ev.1438.
[8]                Dyson, R. G., Allen, R., Camanho, A. S., Podinovski, V. V., Sarrico, C. S., Shale, E. A.,  Pitfalls and protocols in DEA, European Journal of Operational Research, 2001, 132(2), P. 245-259. Doi; 10.1016/S0377-2217(00)00149-1.
[9]                    Doyle, J., and Green, R., Efficiency and Cross-efficiency in DEA: Derivations, Meanings and Uses, Journal of the Operational Research Society, 1994,45(5), P. 567–578. Doi:10.1057/jors.1994.84.
[10]             Green, R., Doyle, J., Cook, W.D., Preference voting and project ranking using DEA and cross-evaluation, European Journal of Operational Research, 1996, 90, P. 461–472. Doi: 10.1016/0377-2217(95)00039-9.
[11]             Arsad, R., Nasir Abdullah, M., Alias, S., and Isa, Z., Selection Input Output by Restriction Using DEA Models Based on a Fuzzy Delphi Approach and Expert Information, Journal of Physics: Conference Series, 2017, 892, 012010. Doi: 10.1088/1742-6596/892/1/012010.
[13]              Sadidi, M., Khalilifar, O., Amiri, M., and Moradi, R., Use of Partial Least Squares  Structural Equation Modeling for Identifying the Most Important Variables via Application of Data Envelopment Analysis, J Arch Mil Med, 2018, 6(1) P. 1-9. Doi: 10.5812/jamm.67114.
[14]             Xie, Q., Dai, Q., Li, Y., and Jiang, A., Increasing the Discriminatory Power of DEA Using Shannon’s Entropy, Entropy, 2014, 16(3), P. 1571–1585. Doi:10.3390/e16031571.
[15]             Adler, N., Golany, B., Including principal component weights to improve discrimination in data envelopment analysis. Journal of the Operational Research Society, 2002, 53(9), P. 985-991. Doi: 10.1057/palgrave.jors.2601400.
[16]             Azadeh, A., Ghaderi, S.F., and Ebrahimipour, V., An integrated PCA DEA framework for assessment and ranking of manufacturing systems based on equipment performance, Engineering Computations (Swansea, Wales), 2007, 24(4), P. 347-372. Doi: 10.1108/02644400710748689.
[17]             Aliakbarpoor, Z., Izadikhah, M., Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis, International Journal of Automation and Computing, 2012, 9 (6), 609-615. DOI: 10.1007/s11633-012-0686-5
[18]             Nguyen, T.T., and Nguyen, P.K., Reducing Attributes in Rough Set Theory with the Viewpoint of Mining Frequent Patterns, International Journal of Advanced Computer Science and Applications, 2013, 4(4), P. 130-138. Doi: 10.14569/IJACSA.2013.040421.
[19]             Markowitz, H.M., Portfolio selection, The Journal of Finance, 1952, 7(1), P. 77–91. Doi: 10.1111/j.1540-6261.1952.tb01525.x.
[20]             Lee, S.M., and Lerro, A.J., Optimaizing the portfolio selection for mutual funds, The Journal of Finance, 1973, 28(5), P. 1087-1101. Doi: 10.1007/978-3-642-59132-7_46.
[21]             Murthi, B.P.S, Choi, Y.K., and Desai, P., Efficiency of Mutual Funds and Portfolio Performance Measurement: A Non - Parametric Approach, European Journal of Operational Research, 1997, 98 (2), P. 408-418. Doi: 10.1016/S0377-2217(96)00356-6.
[22]             Haslem, J. M., and Scheraga, C.A., Data Envelopment Analysis of Morningstar's Large-cap Mutual Funds, The Journal of Investing, 2003, 12(4): 41-48. Doi: 10.3905/joi.2003.319566.
[23]             Edirisinghe, N.C.P., and Zhang, X., Generalized DEA model of fundamental analysis and its application to portfolio optimization, Journal of Banking & Finance, 2007, 31(11): 3311-3335. Doi: 10.1016/j. jbankfin.2007.04.008.
[24]             Hung Chen, H., Stock selection using data envelopment analysis. Industrial Management & Data Systems, 2008,108(9), P. 1255-1268. Doi: 10.1108/02635570810914928.
[25]             Lim, S., Oh, K.W., and Zhu, J., Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market, European Journal of Operational Research, 2014, 236(1), P. 361-368. Doi: 10.1016/j.ejor.2013.12.002.
[26]             Liu, W., Zhoua, Z., Liu, D., and Xiao, H., Estimation of portfolio efficiency via DEA, Omega, 2015, 52, P. 107-118. Doi; 10.1016/
[27]             Choi, H.S., and Min, D., Efficiency of well-diversified portfolios: Evidence from data envelopment analysis, Omega, 2017, 73, P. 104-113. Doi: 10.1016/
[28]             Esfandiar, M., Saremi M., and Jahangiri Nia, H., Assessment of the efficiency of banks accepted in Tehran Stock Exchange using the data envelopment analysis technique, Advances in Mathematical Finance and Applications,2018, 3(2), P. 1-11. Doi: 10.22034/AMFA.2018.540815.
[29]             Izadikhah, M., Improving the Banks Shareholder Long Term Values by Using Data Envelopment Analysis Model. Advances in Mathematical Finance and Applications, 2018, 3(2), P. 27-41. Doi: 10.22034/AMFA.2 018.540829.
[30]             Tarnaud, A.C., and Leleu, H., Portfolio analysis with DEA: Prior to choosing a model, Omega, 2018, 75, P. 57-76. Doi: 10.1016/
[31]             Zhang, Y.J., and Chen, M.Y., Evaluating the dynamic performance of energy portfolios: Empirical evidence from the DEA directional distance function, European Journal of Operational Research, 2018, 269(1), P. 64-78. Doi: 10.1016/j.ejor.2017.08.008.
[32]             Peykani, P., Mohammadi, E., Rostamy-Malkhalifeh, M., and Hosseinzadeh Lotfi, F., Fuzzy Data Envelopment Analysis Approach for Ranking of Stocks with an Application to Tehran Stock Exchange, Advances in Mathematical Finance and Applications,2019, 4(1), P. 31-43. Doi: 10.22034/AMFA.20 19.581412.1155.
[33]             Peykani, P., Mohammadi, E., Pishvaee, M.S., Rostamy-Malkhalifeh, M. and Jabbarzadeh, A., A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches, RAIRO-Operations Research, 2018, 52(4), P.1445-1463. Doi: 10.1051/ro/2018019.
[34]             Charnes, A., Cooper, W.W., and Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 1978, 2(6), P. 429–444. Doi: 10.1016/0377-2217(78)90138-8.
[35]             Banker, R.D., Charnes, A., and Cooper, W.W., Some models for estimating technical and scale efficiencies in date envelopment analysis, Management Science, 1984, 30, P. 1078-1092. Doi: 10.1287/ mnsc.30.9.1078.
[36]             Chambers, R.G., Chung, Y., and Färe, R., Profit, Directional Distance Functions, and Nerlovian Efficiency, Journal of Optimization Theory and Applications, 1998, 98(2), P. 351–364. Doi: 10.1023/A:10 22637501082.
[37]             Khoveyni, M., Eslami, R., Yang, G.l., Negative data in DEA: Recognizing congestion and specifying the least and the most congested decision making units, Computers & Operations Research, 2017, 79, P. 39-48. Doi: 10.1016/j.cor.2016.09.002.
[38]             Tavana, M., Izadikhah, M., Di Caprio, D., Saen, R. F., A new dynamic range directional measure for two-stage data envelopment analysis models with negative data, Computers & Industrial Engineering, 2018, 115, P. 427-448. Doi: 10.1016/j.cie.2017.11.024.
[39]             Lin, R., Yang, W., Huang, H., A modified slacks-based super-efficiency measure in the presence of negative data, Computers & Industrial Engineering, 2019, 135, P. 39-52. Doi: 10.1016/j.cie.201 9.05.030.
[40]             Izadikhah, M., Saen, R.F., Evaluating sustainability of supply chains by two-stage range directional measure in the presence of negative data, Transportation Research Part D: Transport and Environment, 2016, 49, P.110-126. Doi: 10.1016/j.trd.2016.09.003.
[41]             Mehdiloozad, M., Zhu, J., Sahoo, B. K., Identification of congestion in data envelopment analysis under the occurrence of multiple projections: A reliable method capable of dealing with negative data, European Journal of Operational Research, 2018, 265(2), P. 644-654. Doi: 10.1016/j.ejor.2017.07.065.
[42]             Izadikhah, M., Saen, R.F., Roostaee, R., How to assess sustainability of suppliers in the presence of volume discount and negative data in data envelopment analysis?, Annals of Operations Research, 2018, 269(1-2),P. 241-267. Doi:10.1007/s10479-018-2790-6.
[43]             Allahyar, M., and Rostamy-malkhalifeh, M., Negative data in data envelopment analysis: Efficiency analysis and estimating returns to scale. Computers & Industrial Engineering, 2014, 82, P.78-81. Doi: 10.1016/j.cie.2015.01.022.
[44]             Pawlak, Z., Rough Sets, International Journal of Computer and Information Science, 1982, 11(5), P. 341- 356. Doi: 10.1007/BF01001956.
[45]             Pawlak, Z., Rough sets and intelligent data analysis, Information Sciences, 2002, 147(1), P. 1-12. Doi: 10.1016/S0020-0255(02)00197-4.
[46]             Zhang, Q., Xie, Q., and Wang G., A Survey on Rough Set Theory and Its Applications, CAAI Transactions on Intelligence Technology, 2016, 1(4), P. 323-333. Doi: 10.1016/j.trit.2016.11.001.
[47]             Jensen, R., Shen, Q., and Tuson, A., Finding Rough Set Reducts with SAT. In: Ślęzak D., Wang G., Szczuka M., Düntsch I., Yao Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science, vol 3641, Springer, Berlin, Heidelberg, 2005. Doi: 10.1007/11 548669_21.
[48]             Peters, J.F., and Skowron, A., Transactions on Rough Sets XVII, Springer-Verlag Berlin Heidelberg, 2014. Doi: 10.1007/978-3-642-54756-0.
Volume 5, Issue 1
January 2020
Pages 53-67
  • Receive Date: 11 May 2019
  • Revise Date: 16 July 2019
  • Accept Date: 24 July 2019
  • First Publish Date: 01 January 2020