Research Article Designing an Intuitionistic Fuzzy Network Data Envelopment Analysis Model for Efficiency Evaluation of Decision-Making Units with Two-Stage Structures Naﬁseh Javaherian , 1 Ali Hamzehee , 1 and Hossein Sayyadi Tooranloo 2 1 Department of Applied Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran 2 Department of Management, Meybod University, Meybod, Iran CorrespondenceshouldbeaddressedtoAliHamzehee;hamzehee_ali@yahoo.com Received 26 June 2020; Revised 6 October 2020; Accepted 18 December 2020; Published 7 January 2021 AcademicEditor:JoseA.Sanz Copyright©2021NaﬁsehJavaherianetal.isisanopenaccessarticledistributedundertheCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Data envelopment analysis (DEA) is a powerful tool for evaluating the eﬃciency of decision-making units for ranking and comparisonpurposesandtodiﬀerentiateeﬃcientandineﬃcientunits.ClassicDEAmodelsareill-suitedfortheproblemswhere decision-makingunitsconsistofmultiplestageswithintermediateproductsandthosewhereinputsandoutputsareimpreciseor nondeterministic,whichisnotuncommonintherealworld.ispaperpresentsanewDEAmodelforevaluatingtheeﬃciencyof decision-makingunitswithtwo-stagestructuresandtriangularintuitionisticfuzzydata.epaperﬁrstintroducestwo-stageDEA models,thenexplainshowthesemodelscanbemodiﬁedwithintuitionisticfuzzycoeﬃcients,andﬁnallydescribeshowarithmetic operatorsforintuitionisticfuzzynumberscanbeusedforaconversionintocrisptwo-stagestructures.Intheend,theproposed method is used to solve an illustrative numerical example. 1.Introduction Data envelopment analysis is a standard quantitative tool withextensiveuseineﬃciencyevaluationsandperformance analysis [1]. DEA measures the relative eﬃciency of deci- sion-makingunits(DMUs)withsimilarinputsandoutputs in order to give an estimation of how eﬃcient a unit is in comparison with other units [2–4]. However, most of the commonly used DEA models are criticized for treating units as black boxes and ignoring their internal processes, the eﬃciency of these processes, and their relationships[5,6].isblackboxapproachcausestheanalysis tomissalotofvaluableinformationaboutDMUsandlimitsits scope to the fundamental inputs and the ultimate outputs [7]. To address this issue, F¨ areet al. [8] introduced network data envelopment analysis (NDEA) and explained its importance for having a more accurate eﬃciency analysis of DMUs. Unlike traditional DEA models, NDEA models have no ﬁxedformulationandcanbedevelopedintodiﬀerentforms based on the type of process and network structure [9]. NDEA can very well illustrate the relationships and inter- dependencies between internal processes and accurately calculatetheoveralleﬃciencyaswellastheeﬃciencyineach stage [3, 10]. In addition, this method can be used for ac- curate tracking of the sources of ineﬃciency in ineﬃcient units [11]. e two-stage network structure is one of the NDEA topologies that has been extensively studied by re- searchers [12–15]. Typically, data in DEA models are crisp and deter- ministic, but given the high frequency of uncertainties in real-world problems and impreciseness in real-world data, onesimplycannotdependonclassicalmathematicstosolve theseproblems.esolutiontothisissueistousethegray dimensionofclassicallogic,whichisfuzzylogic,toimprove theresultsofthemodels.etheoryoffuzzysets,whichisan extended version of crisp sets, was ﬁrst proposed by Zadeh [16], originally with the purpose of developing a more ef- ﬁcient model for use in natural language processing. Hindawi Advances in Fuzzy Systems Volume 2021, Article ID 8860634, 15 pages https://doi.org/10.1155/2021/8860634