Efficiencya Assessment and Target Setting Using a Fully Fuzzy DEA Approach

Arana‐Jiménez, Manuel; Sánchez-Gil, M. Carmen; Lozano, Sebastián

doi:10.1007/s40815-020-00821-0

Cited by 12 publications

(14 citation statements)

References 31 publications

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“…Bagheri et al [6] proposed a fuzzy data envelopment analysis approach for solving fuzzy multi objective transportation problem. Arana-Jiménez et al [3] proposed a new radial, input-oriented and fully fuzzy DEA approach for assessing the relative efficiency of a set of DMUs. Singh and Pant [64] proposed a fuzzy DEA approach for analyzing the performance of eight selected paper mills of India.…”

Section: Literature Reviewmentioning

confidence: 99%

“…To provide full ranking of performance for the 12 DMUs, Tables 5 and 6 show the values of S α min and S α max at different levels of α ∈ (0, 1] calculated by Eqs. (3) and 5, respectively. Table 7 shows the relative closeness for the twelve DMUs at different levels of α ∈ (0, 1] calculated by Eq.…”

Section: Numerical Examplementioning

confidence: 99%

“…(2) In contrast to most existing approaches, which provide crisp efficiency measures, the developed fuzzy framework provides fuzzy efficiency measures. (3) In contrast to existing method [26], two virtual fuzzy DMUs called fuzzy ideal DMU (FIDMU) and fuzzy anti-ideal DMU (FADMU) are introduced into fuzzy DEA (FDEA) in the presence of undesirable outputs. (4) In contrast to existing method [26,50], the exact form of membership function of the fuzzy relative closeness is determined to give an overall assessment of each DMU.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points

Ebrahimnejad

Amani

2020

Complex Intell. Syst.

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Data envelopment analysis (DEA) is a prominent technique for evaluating relative efficiency of a set of entities called decision making units (DMUs) with homogeneous structures. In order to implement a comprehensive assessment, undesirable factors should be included in the efficiency analysis. The present study endeavors to propose a novel approach for solving DEA model in the presence of undesirable outputs in which all input/output data are represented by triangular fuzzy numbers. To this end, two virtual fuzzy DMUs called fuzzy ideal DMU (FIDMU) and fuzzy anti-ideal DMU (FADMU) are introduced into proposed fuzzy DEA framework. Then, a lexicographic approach is used to find the best and the worst fuzzy efficiencies of FIDMU and FADMU, respectively. Moreover, the resulting fuzzy efficiencies are used to measure the best and worst fuzzy relative efficiencies of DMUs to construct a fuzzy relative closeness index. To address the overall assessment, a new approach is proposed for ranking fuzzy relative closeness indexes based on which the DMUs are ranked. The developed framework greatly reduces the complexity of computation compared with commonly used existing methods in the literature. To validate the proposed methodology and proposed ranking method, a numerical example is illustrated and compared the results with an existing approach.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points

Ebrahimnejad

Amani

2020

Complex Intell. Syst.

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“…Moreover, it makes use of a fuzzy partial order, which has proved to be a flexible FDEA modelling tool ( e.g. [4]). This combination of features leads to a simple and elegant linear programming (LP) formulation that provides crisp e ciency scores as well as fuzzy targets.…”

Section: Introductionmentioning

confidence: 99%

A fuzzy DEA slacks-based approach

Arana‐Jiménez

Sánchez-Gil

Lozano

2022

Journal of Computational and Applied Mathematics

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This paper deals with the problem of e ciency assessment using Data Envelopment Analysis (DEA) when the input and output data are given as fuzzy sets. In particular, a fuzzy extension of the measure of ine ciency proportions, a well-known slacks-based additive ine ciency measure, is considered.The proposed approach also provides fuzzy input and output targets. Computational experiences and comparison with other fuzzy DEA approaches are reported.

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“…These improvements help managers with some helpful information on the variables, and thus they can concentrate their efforts by which the progress can be possible. Arana et al [6] proposed a radial two-phase input-oriented FDEA approach on the trapezoidal fuzzy numbers. The approach explicitly implements the LUfuzzy partial order.…”

Section: Introductionmentioning

confidence: 99%

A novel fuzzy non-radial data envelopment analysis: An application in transportation

2021

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The slack-based measure (SBM) DEA model is a non-radial model used to calculate the relative efficiency, input, and output targets of the different decision-making units (DMUs) based on their best peers or efficient frontier. The conventional SBM DEA model used crisp inputs and outputs. But, it can be observed in real-life problems that sometimes the available data is in linguistic forms such as ‘few,’ ‘many,’ ‘small,’ or missing data. The DEA technique is frontier based, and therefore, imprecise data may lead to untenable results. Fuzzy theory, which is already established to handle uncertain data, can overcome this problem. Furthermore, the sensitivity and stability analysis have been checked the robustness of fuzzy DEA models. In this study, sensitivity and stability analysis of the fuzzy SBM DEA has been performed. The lower and upper sensitive bounds for inputs and outputs variables have been obtained for both the inefficient and efficient DMUs to calculate the input and output targets. Finally, a real-life transportation problem for the validity of the study is presented for its depiction.

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Efficiencya Assessment and Target Setting Using a Fully Fuzzy DEA Approach

Cited by 12 publications

References 31 publications

Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points

Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points

A fuzzy DEA slacks-based approach

A novel fuzzy non-radial data envelopment analysis: An application in transportation

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