{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:24:14Z","timestamp":1785410654619,"version":"3.56.0"},"reference-count":125,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,7,14]],"date-time":"2022-07-14T00:00:00Z","timestamp":1657756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MAKE"],"abstract":"<jats:p>The purpose of this study is to provide an efficient method for the selection of input\u2013output indicators in the data envelopment analysis (DEA) approach, in order to improve the discriminatory power of the DEA method in the evaluation process and performance analysis of homogeneous decision-making units (DMUs) in the presence of negative values and data. For this purpose, the Shannon entropy technique is used as one of the most important methods for determining the weight of indicators. Moreover, due to the presence of negative data in some indicators, the range directional measure (RDM) model is used as the basic model of the research. Finally, to demonstrate the applicability of the proposed approach, the food and beverage industry has been selected from the Tehran stock exchange (TSE) as a case study, and data related to 15 stocks have been extracted from this industry. The numerical and experimental results indicate the efficacy of the hybrid data envelopment analysis\u2013Shannon entropy (DEASE) approach to evaluate stocks under negative data. Furthermore, the discriminatory power of the proposed DEASE approach is greater than that of a classical DEA model.<\/jats:p>","DOI":"10.3390\/make4030032","type":"journal-article","created":{"date-parts":[[2022,7,15]],"date-time":"2022-07-15T01:57:11Z","timestamp":1657850231000},"page":"688-699","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Input\/Output Variables Selection in Data Envelopment Analysis: A Shannon Entropy Approach"],"prefix":"10.3390","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7486-6796","authenticated-orcid":false,"given":"Pejman","family":"Peykani","sequence":"first","affiliation":[{"name":"School of Industrial Engineering, Iran University of Science and Technology, Tehran 1684613114, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fatemeh Sadat","family":"Seyed Esmaeili","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2679-0488","authenticated-orcid":false,"given":"Mirpouya","family":"Mirmozaffari","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, Dalhousie University, 5269 Morris Street, Halifax, NS B3H 4R2, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Armin","family":"Jabbarzadeh","sequence":"additional","affiliation":[{"name":"Department of Systems Engineering, \u00c9cole de Technologie Sup\u00e9rieure (ETS), University of Quebec, 1100 Notre-Dame Street West, Montreal, QC H3C 1K3, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Khamechian","sequence":"additional","affiliation":[{"name":"Department of Industrial and Manufacturing Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"253","DOI":"10.2307\/2343100","article-title":"The measurement of productive efficiency","volume":"120","author":"Farrell","year":"1957","journal-title":"J. R. Stat. Soc. Ser. A (Gen.)"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/0377-2217(78)90138-8","article-title":"Measuring the efficiency of decision making units","volume":"2","author":"Charnes","year":"1978","journal-title":"Eur. J. Oper. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1078","DOI":"10.1287\/mnsc.30.9.1078","article-title":"Some models for estimating technical and scale inefficiencies in data envelopment analysis","volume":"30","author":"Banker","year":"1984","journal-title":"Manag. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/BF01874733","article-title":"Preface to topics in data envelopment analysis","volume":"2","author":"Charnes","year":"1985","journal-title":"Ann. Oper. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.omega.2015.04.004","article-title":"Research fronts in data envelopment analysis","volume":"58","author":"Liu","year":"2016","journal-title":"Omega"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/j.omega.2012.11.004","article-title":"A survey of DEA applications","volume":"41","author":"Liu","year":"2013","journal-title":"Omega"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"e12721","DOI":"10.1111\/exsy.12721","article-title":"Window data envelopment analysis approach: A review and bibliometric analysis","volume":"38","author":"Peykani","year":"2021","journal-title":"Expert Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.omega.2011.08.010","article-title":"A survey on bank branch efficiency and performance research with data envelopment analysis","volume":"41","author":"Paradi","year":"2013","journal-title":"Omega"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1016\/j.im.2014.05.009","article-title":"Efficiency analysis of information technology and online social networks management: An integrated DEA-model assessment","volume":"51","year":"2014","journal-title":"Inf. Manag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.rser.2014.07.153","article-title":"A DEA approach for estimating the agricultural energy and environmental efficiency of EU countries","volume":"40","author":"Vlontzos","year":"2014","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/1573062X.2013.765488","article-title":"A review of frontier approaches to efficiency and productivity measurement in urban water utilities","volume":"11","author":"Worthington","year":"2014","journal-title":"Urban Water J."},{"key":"ref_12","first-page":"9","article-title":"Recent DEA applications to industry: A literature review from 2010 to 2014","volume":"4","year":"2015","journal-title":"Int. J. Eng. Sci. Invent."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Basso, A., and Funari, S. (2016). DEA performance assessment of mutual funds. Data Envelopment Analysis, Springer.","DOI":"10.1007\/978-1-4899-7684-0_8"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1108\/IJPPM-06-2015-0090","article-title":"Measuring business performance in the airport context: A critical review of literature","volume":"65","author":"Fasone","year":"2016","journal-title":"Int. J. Product. Perform. Manag."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Thanassoulis, E., Witte, K.D., Johnes, J., Johnes, G., Karagiannis, G., and Portela, C.S. (2016). Applications of data envelopment analysis in education. Data Envelopment Analysis, Springer.","DOI":"10.1007\/978-1-4899-7684-0_12"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s10479-016-2294-1","article-title":"Data envelopment analysis in financial services: A citations network analysis of banks, insurance companies and money market funds","volume":"253","author":"Kaffash","year":"2017","journal-title":"Ann. Oper. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.cie.2017.09.022","article-title":"Quantitative models for supply chain performance evaluation: A literature review","volume":"113","author":"Carpinetti","year":"2017","journal-title":"Comput. Ind. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1298","DOI":"10.1016\/j.rser.2016.12.030","article-title":"A comprehensive review of data envelopment analysis (DEA) approach in energy efficiency","volume":"70","author":"Mardani","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1007\/s10479-017-2605-1","article-title":"Application of data envelopment analysis models in supply chain management: A systematic review and meta-analysis","volume":"271","author":"Soheilirad","year":"2018","journal-title":"Ann. Oper. Res."},{"key":"ref_20","first-page":"82","article-title":"A comprehensive review of data envelopment analysis (DEA). Approach in sports","volume":"9","author":"Bhat","year":"2019","journal-title":"J. Sports Econ. Manag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1080\/09537325.2018.1493191","article-title":"Evaluating R&D performance of EU countries using categorical DEA","volume":"31","author":"Karadayi","year":"2019","journal-title":"Technol. Anal. Strateg. Manag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s10729-018-9436-8","article-title":"The use of Data Envelopment Analysis (DEA) in healthcare with a focus on hospitals","volume":"22","author":"Kohl","year":"2019","journal-title":"Health Care Manag. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lee, H.S., and Choi, Y. (2019). Environmental performance evaluation of the Korean manufacturing industry based on sequential DEA. Sustainability, 11.","DOI":"10.3390\/su11030874"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2931734","DOI":"10.1155\/2021\/2931734","article-title":"A review of data envelopment analysis in airline efficiency: State of the art and prospects","volume":"2021","author":"Cui","year":"2021","journal-title":"J. Adv. Transp."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1016\/j.ejor.2019.07.034","article-title":"A survey of data envelopment analysis applications in the insurance industry 1993\u20132018","volume":"284","author":"Kaffash","year":"2020","journal-title":"Eur. J. Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"100672","DOI":"10.1016\/j.seps.2018.11.009","article-title":"The origins, development and future directions of data envelopment analysis approach in transportation systems","volume":"69","author":"Mahmoudi","year":"2020","journal-title":"Socio-Econ. Plan. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"102883","DOI":"10.1016\/j.ijhm.2021.102883","article-title":"Tourism, hospitality, and DEA: Where do we come from and where do we go?","volume":"95","author":"Nurmatov","year":"2021","journal-title":"Int. J. Hosp. Manag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0304-4076(90)90045-U","article-title":"Recent developments in DEA: The mathematical programming approach to frontier analysis","volume":"46","author":"Seiford","year":"1990","journal-title":"J. Econom."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1057\/palgrave.jors.2600342","article-title":"Data envelopment analysis theory, methodology and applications","volume":"48","author":"Charnes","year":"1997","journal-title":"J. Oper. Res. Soc."},{"key":"ref_30","first-page":"348","article-title":"Comparative performance measurement: A primer on data envelopment analysis","volume":"22","author":"Nyhan","year":"1999","journal-title":"Public Product. Manag. Rev."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.seps.2007.07.002","article-title":"Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA","volume":"42","author":"Emrouznejad","year":"2008","journal-title":"Socio-Econ. Plan. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Cooper, W.W., Seiford, L.M., and Zhu, J. (2011). Data envelopment analysis: History, models, and interpretations. Handbook on Data Envelopment Analysis, Springer.","DOI":"10.1007\/978-1-4419-6151-8"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10479-014-1535-4","article-title":"Advances in data envelopment analysis","volume":"214","author":"Emrouznejad","year":"2014","journal-title":"Ann. Oper. Res."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Joro, T., and Korhonen, P. (2015). Extension of Data Envelopment Analysis with Preference Information, Springer.","DOI":"10.1007\/978-1-4899-7528-7"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.seps.2017.01.008","article-title":"A survey and analysis of the first 40 years of scholarly literature in DEA: 1978\u20132016","volume":"61","author":"Emrouznejad","year":"2018","journal-title":"Socio-Econ. Plan. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1016\/S0305-0548(97)00102-0","article-title":"Combining ranking scales and selecting variables in the DEA context: The case of industrial branches","volume":"25","author":"Friedman","year":"1998","journal-title":"Comput. Oper. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/S0377-2217(00)00149-1","article-title":"Pitfalls and protocols in DEA","volume":"132","author":"Dyson","year":"2001","journal-title":"Eur. J. Oper. Res."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Sarkis, J. (2007). Preparing your data for DEA. Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis, Springer.","DOI":"10.1007\/978-0-387-71607-7_17"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1016\/j.ejor.2010.06.027","article-title":"Input\/output selection in DEA under expert information, with application to financial markets","volume":"207","author":"Edirisinghe","year":"2010","journal-title":"Eur. J. Oper. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1016\/j.eswa.2011.07.111","article-title":"Input\/output indicator selection for DEA efficiency evaluation: An empirical study of Chinese commercial banks","volume":"39","author":"Luo","year":"2012","journal-title":"Expert Syst. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1892","DOI":"10.1108\/BIJ-07-2015-0074","article-title":"Generalized DEA: An approach for supporting input\/output factor determination in DEA","volume":"23","author":"Afsharian","year":"2016","journal-title":"Benchmarking Int. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"5146","DOI":"10.1016\/j.eswa.2008.06.031","article-title":"Shannon\u2019s entropy for combining the efficiency results of different DEA models: Method and application","volume":"36","author":"Zarepisheh","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1909","DOI":"10.1016\/j.enpol.2009.11.071","article-title":"Resource and environment efficiency analysis of provinces in China: A DEA approach based on Shannon\u2019s entropy","volume":"38","author":"Bian","year":"2010","journal-title":"Energy Policy"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"6726","DOI":"10.1080\/00207543.2011.618150","article-title":"DEA cross-efficiency aggregation method based upon Shannon entropy","volume":"50","author":"Wu","year":"2012","journal-title":"Int. J. Prod. Res."},{"key":"ref_45","first-page":"149","article-title":"Aggregating the results of ranking models in data envelopment analysis by Shannon\u2019s entropy: A case study in hotel industry","volume":"3","author":"Shirouyehzad","year":"2013","journal-title":"Int. J. Model. Oper. Manag."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"6394","DOI":"10.3390\/e16126394","article-title":"Determining common weights in data envelopment analysis with Shannon\u2019s entropy","volume":"16","author":"Qi","year":"2014","journal-title":"Entropy"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.3390\/e16031571","article-title":"Increasing the discriminatory power of DEA using Shannon\u2019s entropy","volume":"16","author":"Xie","year":"2014","journal-title":"Entropy"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Lo Storto, C. (2016). Ecological efficiency based ranking of cities: A combined DEA cross-efficiency and Shannon\u2019s entropy method. Sustainability, 8.","DOI":"10.3390\/su8020124"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1007\/s11269-015-1169-6","article-title":"Application of integrated Shannon\u2019s entropy and VIKOR techniques in prioritization of flood risk in the Shemshak watershed, Iran","volume":"30","author":"Malekian","year":"2016","journal-title":"Water Resour. Manag."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1016\/j.renene.2016.12.062","article-title":"Evaluation of relative impact of aerosols on photovoltaic cells through combined Shannon\u2019s entropy and Data Envelopment Analysis (DEA)","volume":"105","author":"Ghosh","year":"2017","journal-title":"Renew. Energy"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1111\/itor.12361","article-title":"An improvement in DEA cross-efficiency aggregation based on the Shannon entropy","volume":"25","author":"Song","year":"2018","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Feutrill, A., and Roughan, M. (2021). A Review of Shannon and Differential Entropy Rate Estimation. Entropy, 23.","DOI":"10.3390\/e23081046"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"8730264","DOI":"10.1155\/2021\/8730264","article-title":"Research on World Food Production Efficiency and Environmental Sustainability Based on Entropy-DEA Model","volume":"2021","author":"Zhang","year":"2021","journal-title":"Complexity"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1108\/10176749710368217","article-title":"An evaluation of the relative performance of university libraries in Taipei","volume":"6","author":"Chen","year":"1997","journal-title":"Asian Libr."},{"key":"ref_55","unstructured":"Avkiran, N.K. (1999). Productivity Analysis in the Services Sector with Data Envelopment Analysis, SSRN."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1300\/J073v16n02_04","article-title":"Using data envelopment analysis for measuring and benchmarking productivity in the hotel sector","volume":"16","author":"Sigala","year":"2004","journal-title":"J. Travel Tour. Mark."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/j.tre.2011.01.001","article-title":"The relative efficiency of shipping companies","volume":"47","author":"Panayides","year":"2011","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1108\/14635771111109832","article-title":"Benchmarking of North Indian urban water utilities","volume":"18","author":"Singh","year":"2011","journal-title":"Benchmarking Int. J."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.omega.2010.09.002","article-title":"Stochastic simulation based genetic algorithm for chance constrained data envelopment analysis problems","volume":"39","author":"Udhayakumar","year":"2011","journal-title":"Omega"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"530","DOI":"10.1016\/j.enconman.2015.09.072","article-title":"Benchmarking energy performance of residential buildings using two-stage multifactor data envelopment analysis with degree-day based simple-normalization approach","volume":"106","author":"Wang","year":"2015","journal-title":"Energy Convers. Manag."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1080\/21649502.2016.1262938","article-title":"Modeling the efficiency of universal banks in Ghana","volume":"4","author":"Adusei","year":"2016","journal-title":"Quant. Financ. Lett."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1080\/03088839.2017.1298863","article-title":"Integrating multi-stage data envelopment analysis and a fuzzy analytical hierarchical process to evaluate the efficiency of major global liner shipping companies","volume":"44","author":"Chao","year":"2017","journal-title":"Marit. Policy Manag."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Shah, S.A.R., Brijs, T., Ahmad, N., Pirdavani, A., Shen, Y., and Basheer, M.A. (2017). Road safety risk evaluation using GIS-based data envelopment analysis\u2014Artificial neural networks approach. Appl. Sci., 7.","DOI":"10.3390\/app7090886"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Hwang, Y.G., Park, S., and Kim, D. (2018). Efficiency analysis of official development assistance provided by Korea. Sustainability, 10.","DOI":"10.3390\/su10082697"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Jiang, H., and He, Y. (2018). Applying data envelopment analysis in measuring the efficiency of Chinese listed banks in the context of macroprudential framework. Mathematics, 6.","DOI":"10.3390\/math6100184"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Sevin\u00e7, A., and Eren, T. (2019). Determination of KOSGEB support models for small-and medium-scale enterprises by means of data envelopment analysis and multi-criteria decision making methods. Processes, 7.","DOI":"10.3390\/pr7030130"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1057\/palgrave.jors.2601768","article-title":"Negative Data in DEA: A Directional Distance Approach Applied to Bank Branches","volume":"55","author":"Portela","year":"2004","journal-title":"J. Oper. Res. Soc."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"3311","DOI":"10.1016\/j.jbankfin.2007.04.008","article-title":"Generalized DEA model of fundamental analysis and its application to portfolio optimization","volume":"31","author":"Edirisinghe","year":"2007","journal-title":"J. Bank. Financ."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1057\/palgrave.jors.2602442","article-title":"Portfolio selection under DEA-based relative financial strength indicators: Case of US industries","volume":"59","author":"Edirisinghe","year":"2008","journal-title":"J. Oper. Res. Soc."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"3187","DOI":"10.1016\/j.cor.2009.02.009","article-title":"A multicriteria methodology for equity selection using financial analysis","volume":"36","author":"Xidonas","year":"2009","journal-title":"Comput. Oper. Res."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.ejor.2013.12.002","article-title":"Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market","volume":"236","author":"Lim","year":"2014","journal-title":"Eur. J. Oper. Res."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.asoc.2015.09.018","article-title":"An integrated multi-objective Markowitz\u2013DEA cross-efficiency model with fuzzy returns for portfolio selection problem","volume":"38","author":"Mashayekhi","year":"2016","journal-title":"Appl. Soft Comput."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.qref.2018.11.008","article-title":"Comparing relative valuation efficiency between two stock markets","volume":"72","author":"Yi","year":"2019","journal-title":"Q. Rev. Econ. Financ."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.omega.2013.09.004","article-title":"Data envelopment analysis: Prior to choosing a model","volume":"44","author":"Cook","year":"2014","journal-title":"Omega"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1007\/s40685-018-0077-z","article-title":"Is data envelopment analysis a suitable tool for performance measurement and benchmarking in non-production contexts?","volume":"12","author":"Wojcik","year":"2019","journal-title":"Bus. Res."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.ejor.2011.02.001","article-title":"A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making","volume":"214","author":"Emrouznejad","year":"2011","journal-title":"Eur. J. Oper. Res."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1051\/ro\/2018019","article-title":"A novel fuzzy data envelopment analysis based on robust possibilistic programming: Possibility, necessity and credibility-based approaches","volume":"52","author":"Peykani","year":"2018","journal-title":"RAIRO-Oper. Res."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.eswa.2019.06.039","article-title":"Fuzzy data envelopment analysis: An adjustable approach","volume":"136","author":"Peykani","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"3225","DOI":"10.1007\/s00500-020-05374-w","article-title":"Development of two-stage parallel-series system with fuzzy data: A fuzzy DEA approach","volume":"25","author":"Arya","year":"2021","journal-title":"Soft Comput."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"113938","DOI":"10.1016\/j.eswa.2020.113938","article-title":"An adjustable fuzzy chance-constrained network DEA approach with application to ranking investment firms","volume":"166","author":"Peykani","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_81","first-page":"12","article-title":"Optimistic and pessimistic fuzzy data envelopment analysis: Empirical evidence from Tehran stock market","volume":"2","author":"Peykani","year":"2021","journal-title":"Fuzzy Optim. Modeling J."},{"key":"ref_82","first-page":"191","article-title":"A novel mathematical approach for fuzzy multi-period multi-objective portfolio optimization problem under uncertain environment and practical constraints","volume":"2","author":"Peykani","year":"2021","journal-title":"J. Fuzzy Ext. Appl."},{"key":"ref_83","first-page":"10","article-title":"Malmquist productivity index under fuzzy environment","volume":"2","author":"Peykani","year":"2021","journal-title":"Fuzzy Optim. Modeling J."},{"key":"ref_84","doi-asserted-by":"crossref","unstructured":"Song, J., Ma, X., and Chen, R. (2021). A Profit Distribution Model of Reverse Logistics Based on Fuzzy DEA Efficiency\u2014Modified Shapley Value. Sustainability, 13.","DOI":"10.3390\/su13137354"},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Wu, S.C., Lu, T., and Liu, S.T. (2021). A fuzzy approach to support evaluation of fuzzy cross efficiency. Symmetry, 13.","DOI":"10.3390\/sym13050882"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"113180","DOI":"10.1016\/j.cam.2020.113180","article-title":"A fuzzy DEA slacks-based approach","volume":"404","author":"Lozano","year":"2022","journal-title":"J. Comput. Appl. Math."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s10700-021-09364-x","article-title":"Fuzzy chance-constrained data envelopment analysis: A structured literature review, current trends, and future directions","volume":"21","author":"Peykani","year":"2022","journal-title":"Fuzzy Optim. Decis. Mak."},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Peykani, P., Memar-Masjed, E., Arabjazi, N., and Mirmozaffari, M. (2022). Dynamic performance assessment of hospitals by applying credibility-based fuzzy window data envelopment analysis. Healthcare, 10.","DOI":"10.3390\/healthcare10050876"},{"key":"ref_89","doi-asserted-by":"crossref","unstructured":"Peykani, P., Namakshenas, M., Nouri, M., Kavand, N., and Rostamy-Malkhalifeh, M. (2022). A possibilistic programming approach to portfolio optimization problem under fuzzy data. Advances in Econometrics, Operational Research, Data Science and Actuarial Studies, Springer.","DOI":"10.1007\/978-3-030-85254-2_23"},{"key":"ref_90","doi-asserted-by":"crossref","unstructured":"Peykani, P., Namazi, M., and Mohammadi, E. (2022). Bridging the knowledge gap between technology and business: An innovation strategy perspective. PLoS ONE, 17.","DOI":"10.1371\/journal.pone.0266843"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0304-4076(90)90050-4","article-title":"Transformations in stochastic DEA models","volume":"46","author":"Sengupta","year":"1990","journal-title":"J. Econom."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02187302","article-title":"Satisficing DEA models under chance constraints","volume":"66","author":"Cooper","year":"1996","journal-title":"Ann. Oper. Res."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1023\/A:1007874304917","article-title":"Stochastic DEA models with different types of input-output disturbances","volume":"15","author":"Huang","year":"2001","journal-title":"J. Product. Anal."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1057\/palgrave.jors.2601433","article-title":"Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis","volume":"53","author":"Cooper","year":"2002","journal-title":"J. Oper. Res. Soc."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/j.ejor.2015.07.058","article-title":"Stochastic Data Envelopment Analysis\u2014A Review","volume":"251","author":"Olesen","year":"2016","journal-title":"Eur. J. Oper. Res."},{"key":"ref_96","first-page":"52","article-title":"Stochastic Sensitivity Analysis in Data Envelopment Analysis","volume":"2","author":"Arabjazi","year":"2021","journal-title":"Fuzzy Optim. Modeling J."},{"key":"ref_97","doi-asserted-by":"crossref","unstructured":"Babaie Asil, H., Kazemi Matin, R., Khounsiavash, M., and Moghadas, Z. (2021). A modified semi-oriented radial measure to deal with negative and stochastic data: An application in banking industry. Math. Sci., 1\u201313.","DOI":"10.1007\/s40096-021-00416-2"},{"key":"ref_98","first-page":"281","article-title":"Stochastic Data Envelopment Analysis","volume":"5","author":"Banker","year":"2021","journal-title":"Data Envel. Anal. J."},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1504\/IJOR.2021.115627","article-title":"Developing a new chance constrained modified ERM model to measure performance of repair and maintenance groups of IRALCO","volume":"41","author":"Izadikhah","year":"2021","journal-title":"Int. J. Oper. Res."},{"key":"ref_100","doi-asserted-by":"crossref","unstructured":"Izadikhah, M., and Farzipoor Saen, R. (2021). Developing a linear stochastic two-stage data envelopment analysis model for evaluating sustainability of supply chains: A case study in welding industry. Ann. Oper. Res., 1\u201321.","DOI":"10.1007\/s10479-021-04160-7"},{"key":"ref_101","doi-asserted-by":"crossref","unstructured":"Kao, C., and Liu, S.T. (2021). Stochastic efficiencies of network production systems with correlated stochastic data: The case of Taiwanese commercial banks. Ann. Oper. Res., 1\u201324.","DOI":"10.1007\/s10479-020-03879-z"},{"key":"ref_102","doi-asserted-by":"crossref","unstructured":"Amirteimoori, A., Sahoo, B.K., Charles, V., and Mehdizadeh, S. (2022). Stochastic Data Envelopment Analysis. Stochastic Benchmarking, Springer.","DOI":"10.1007\/978-3-030-89869-4"},{"key":"ref_103","first-page":"343","article-title":"The efficiency of MSBM model with imprecise data (interval)","volume":"2","year":"2014","journal-title":"Int. J. Data Envel. Anal."},{"key":"ref_104","first-page":"63","article-title":"Interval network data envelopment analysis model for classification of investment companies in the presence of uncertain data","volume":"11","author":"Peykani","year":"2018","journal-title":"J. Ind. Syst. Eng."},{"key":"ref_105","first-page":"73","article-title":"Stock evaluation under mixed uncertainties using robust DEA model","volume":"4","author":"Peykani","year":"2019","journal-title":"J. Qual. Eng. Prod. Optim."},{"key":"ref_106","doi-asserted-by":"crossref","first-page":"e12534","DOI":"10.1111\/exsy.12534","article-title":"Data envelopment analysis and robust optimization: A review","volume":"37","author":"Peykani","year":"2020","journal-title":"Expert Syst."},{"key":"ref_107","doi-asserted-by":"crossref","unstructured":"Peykani, P., Mohammadi, E., Jabbarzadeh, A., Rostamy-Malkhalifeh, M., and Pishvaee, M.S. (2020). A novel two-phase robust portfolio selection and optimization approach under uncertainty: A case study of Tehran stock exchange. PLoS ONE, 15.","DOI":"10.1371\/journal.pone.0239810"},{"key":"ref_108","first-page":"103","article-title":"Two-stage network DEA model under interval data","volume":"1","year":"2020","journal-title":"Math. Anal. Convex Optim."},{"key":"ref_109","first-page":"308","article-title":"A hybrid approach using data envelopment analysis, interval programming and robust optimisation for performance assessment of hotels under uncertainty","volume":"20","year":"2021","journal-title":"Int. J. Manag. Decis. Mak."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"115855","DOI":"10.1016\/j.eswa.2021.115855","article-title":"A box-uncertainty in DEA: A robust performance measurement framework","volume":"187","author":"Dehnokhalaji","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_111","doi-asserted-by":"crossref","unstructured":"Peykani, P., Emrouznejad, A., Mohammadi, E., and Gheidar-Kheljani, J. (2022). A novel robust network data envelopment analysis approach for performance assessment of mutual funds under uncertainty. Ann. Oper. Res., 1\u201327.","DOI":"10.1007\/s10479-022-04625-3"},{"key":"ref_112","doi-asserted-by":"crossref","unstructured":"Peykani, P., Gheidar-Kheljani, J., Rahmani, D., Karimi Gavareshki, M.H., and Jabbarzadeh, A. (2022). Uncertain super-efficiency data envelopment analysis. Advances in Econometrics, Operational Research, Data Science and Actuarial Studies, Springer.","DOI":"10.1007\/978-3-030-85254-2_19"},{"key":"ref_113","first-page":"9","article-title":"Interval network Malmquist productivity index for examining productivity changes of insurance companies under data uncertainty: A case study","volume":"16","year":"2022","journal-title":"J. Math. Ext."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.eswa.2019.01.012","article-title":"Literature review: Machine learning techniques applied to financial market prediction","volume":"124","author":"Henrique","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_115","doi-asserted-by":"crossref","unstructured":"Mirmozaffari, M., Shadkam, E., Khalili, S.M., and Yazdani, M. (2021). Developing a novel integrated generalised data envelopment analysis (DEA) to evaluate hospitals providing stroke care services. Bioengineering, 8.","DOI":"10.3390\/bioengineering8120207"},{"key":"ref_116","doi-asserted-by":"crossref","unstructured":"Mirmozaffari, M., Yazdani, M., Boskabadi, A., Ahady Dolatsara, H., Kabirifar, K., and Amiri Golilarz, N. (2020). A novel machine learning approach combined with optimization models for eco-efficiency evaluation. Appl. Sci., 10.","DOI":"10.3390\/app10155210"},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"1120","DOI":"10.3389\/fpls.2020.01120","article-title":"Forecasting corn yield with machine learning ensembles","volume":"11","author":"Shahhosseini","year":"2020","journal-title":"Front. Plant Sci."},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"357","DOI":"10.3390\/make3020018","article-title":"Estimating neural network\u2019s performance with bootstrap: A tutorial","volume":"3","author":"Michelucci","year":"2021","journal-title":"Mach. Learn. Knowl. Extr."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1108\/IJESM-02-2020-0003","article-title":"A novel artificial intelligent approach: Comparison of machine learning tools and algorithms based on optimization DEA Malmquist productivity index for eco-efficiency evaluation","volume":"15","author":"Mirmozaffari","year":"2021","journal-title":"Int. J. Energy Sect. Manag."},{"key":"ref_120","doi-asserted-by":"crossref","unstructured":"Mirmozaffari, M., Yazdani, R., Shadkam, E., Khalili, S.M., Tavassoli, L.S., and Boskabadi, A. (2021). A novel hybrid parametric and non-parametric optimisation model for average technical efficiency assessment in public hospitals during and post-COVID-19 pandemic. Bioengineering, 9.","DOI":"10.3390\/bioengineering9010007"},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.susoc.2021.03.002","article-title":"VCS and CVS: New combined parametric and non-parametric operation research models","volume":"2","author":"Mirmozaffari","year":"2021","journal-title":"Sustain. Oper. Comput."},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"66","DOI":"10.3390\/make4010004","article-title":"A Survey of Near-Data Processing Architectures for Neural Networks","volume":"4","author":"Hassanpour","year":"2022","journal-title":"Mach. Learn. Knowl. Extr."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"446","DOI":"10.3390\/make4020020","article-title":"Machine learning in disaster management: Recent developments in methods and applications","volume":"4","author":"Linardos","year":"2022","journal-title":"Mach. Learn. Knowl. Extr."},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.susoc.2022.01.003","article-title":"An integrated artificial intelligence model for efficiency assessment in pharmaceutical companies during the COVID-19 pandemic","volume":"3","author":"Mirmozaffari","year":"2022","journal-title":"Sustain. Oper. Comput."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"105","DOI":"10.3390\/make4010006","article-title":"Machine learning based restaurant sales forecasting","volume":"4","author":"Schmidt","year":"2022","journal-title":"Mach. Learn. Knowl. Extr."}],"container-title":["Machine Learning and Knowledge Extraction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-4990\/4\/3\/32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:50:43Z","timestamp":1760140243000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-4990\/4\/3\/32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,14]]},"references-count":125,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["make4030032"],"URL":"https:\/\/doi.org\/10.3390\/make4030032","relation":{},"ISSN":["2504-4990"],"issn-type":[{"value":"2504-4990","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,14]]}}}