Possibilistic Data Envelopment Analysis (PDEA) is one of the most applicable and popular approaches in the literature to deal with imprecise and ambiguous data in DEA models. In this approach, with respect to tendency of decision maker (DM) in taking optimistic, pessimistic and compromise attitude, three measures including possibility, necessity and credibility measures are used to form the Fuzzy DEA (FDEA) models, respectively. However, decision makers may have different preference and so it is necessary to customize fuzzy DEA models according to properties of DMUs. This paper proposes a novel fuzzy DEA model based on general fuzzy measure in which the attitude of DMUs could be determined by the optimistic-pessimistic parameters. As a result, the proposed FDEA model is general, applicable, flexible, and adjustable based on each DMUs. A numerical example is used to explain the proposed approach while usefulness and applicability of this approach have been illustrated using a real data set to measure efficiency of 38 hospital in United States.
This paper reviews the milestone approaches for handling uncertainty in data envelopment analysis (DEA). This paper presents the detailed classifications of robust data envelopment analysis (RDEA). RDEA is appropriate for measuring the efficiencies of decision‐making units in the presence of the data and distributional uncertainties. This paper reviews scenario‐based and uncertainty set of DEA models. It covers 73 studies from 2008 to 2019. The paper concludes with suggestions about the guidelines for future researches in the field of RDEA.
Possibilistic programming approach is one of the most popular methods used to cope with epistemic uncertainty in optimization models. In this paper, several robust fuzzy data envelopment analysis (RFDEA) models are proposed by the use of different fuzzy measures including possibility, necessity and credibility measures. Despite the regular fuzzy DEA methods, the proposed models are able to endogenously adjust the confidence level of each constraints and produce both conservative and non-conservative methods based on various fuzzy measures. The developed RFDEA models are then linearized and numerically compared to regular fuzzy DEA models. Illustrative results in all of the FDEA and RFDEA models show that, maximum efficiency is obtained for possibility, credibility and necessity-based models, respectively.
This paper presents a novel approach for performance appraisal and ranking of decision-making units (DMUs) with two-stage network structure in the presence of imprecise and vague data. In order to achieve this goal, two-stage data envelopment analysis (DEA) model, adjustable possibilistic programming (APP), and chanceconstrained programming (CCP) are applied to propose the new fuzzy network data envelopment analysis (FNDEA) approach. The main advantages of the proposed FNDEA approach can be summarized as follows: linearity of the proposed FNDEA models, unique efficiency decomposing under ambiguity, capability to extending for other network structures. Moreover, FNDEA approach can be applied for ranking of two-stage DMUs under fuzzy environment in three stages: 1) solving the proposed FNDEA model for all optimistic-pessimistic viewpoints and confidence levels, 2) then plotting the results and drawing the surface of all efficiency scores, 3) and finally calculate the volume of the three-dimensional shape in below the efficiency surface. This volume can be as ranking criterion. Remarkably, the presented fuzzy network DEA approach is implemented for performance appraisal and ranking of investment firms (IFs) with two-stage processes including operational and portfolio management process. Illustrative results of the real-life case study show that the proposed approach is effective and practically very useful.
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