Fuzzy Data envelopment Analysis with SBM using α-level Fuzzy Approach

The applications of fuzzy analysis in data-oriented techniques are the challenging aspect in the field of applied operational research. The use of fuzzy set theoretic measure is explored here in the context of data envelopment analysis (DEA) where we are utilizing the fuzzy α-level approach in the three types of efficiency models. Namely, BCC models, SBM model and supper efficiency model in DEA. It was observed from the result that the fuzzy SBM model has good discrimination power over fuzzy BCC. On the other side, both the models fuzzy BCC and fuzzy SBM are not able to make the genuine ranking which is acceptable for all. So this weakness is overcome with the help of fuzzy super SBM model and all three models are applied to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is in imprecise. In this paper, we are considering that our inputs and outputs are not known with absolute precision in DEA and here, we using Fuzzy-DEA models based on an α-level fuzzy approach to assessing fuzzy data.

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Double Frontier Two-Stage Fuzzy Data Envelopment Analysis

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488520500063 ◽

2020 ◽

Vol 28 (01) ◽

pp. 117-152 ◽

Cited By ~ 1

Author(s):

Alireza Amirteimoori ◽

Hossein Azizi ◽

Sohrab Kordrostami

Keyword(s):

Decision Making ◽

Data Envelopment Analysis ◽

Efficiency Analysis ◽

Programming Approach ◽

Data Envelopment ◽

Fuzzy Data ◽

Insurance Company ◽

Two Stage ◽

Dea Models ◽

Fuzzy Dea

Data envelopment analysis (DEA) is a mathematical programming approach with widespread applications in productivity and efficiency analysis. Compared with traditional DEA models, two-stage DEA models show the performance of each process and make available more information for decision making. In an article by Kao and Liu, models were proposed for combining a two-stage process to achieve overall fuzzy efficiency measures. Their method follows the simple geometric average approach and uses the product of two efficiencies. The present article applies a different angle for efficiency analysis in the two-stage fuzzy DEA. We suggest that the overall efficiency score of a decision-making unit (DMU) is defined as total weight of stage efficiencies, not as the simple product of their efficiency. Moreover, the proposed fuzzy DEA models are different from the model by Kao and Liu for fuzzy data in that our models are linear without the need for additional changes in variables and use the same set of constraints to measure the efficiency of DMUs with fuzzy input and output data. While the models by Kao and Liu are a nonlinear optimization problem that need additional changes in variables, and use different sets of constraints to measure fuzzy efficiencies. Additionally, our proposed approach evaluates the performance of DMUs from both optimistic and pessimistic viewpoints. Finally, using the proposed approach, the Taiwanese non-life insurance company problem will be investigated.

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Dynamic fuzzy data envelopment analysis models: case of bus transport performance assessment

RAIRO - Operations Research ◽

10.1051/ro/2017064 ◽

2019 ◽

Vol 53 (3) ◽

pp. 991-1005 ◽

Cited By ~ 1

Author(s):

Barbara T.H. Yen ◽

Yu-Chiun Chiou

Keyword(s):

Data Envelopment Analysis ◽

Performance Assessment ◽

Capital Investment ◽

Data Envelopment ◽

Fuzzy Data ◽

Fuzzy Variables ◽

Comparative Efficiency ◽

Fuzzy Data Envelopment Analysis ◽

Dea Models ◽

Bus Transport

In the transport field, two characteristics–inter-temporal dependency and fuzziness–need to be considered when assessing transport performance. First, input and output levels are inter-temporal dependent due to heavy capital investment and because quasi-fixed input can influence output levels over multiple periods. Second, conventional Data Envelopment Analysis (DEA) models are, in nature, formulated with quantitative variables. However, qualitative measurements that are characterized with “vagueness” or “fuzziness” are as important as quantitative variables for multi-period transport performance assessment. To rectify these problems, the present study extends previous research by proposing a Dynamic Fuzzy Data Envelopment Analysis (DFDEA) method for assessing the comparative efficiency where inter-temporal dependence exists in operating production processes with some “fuzzy” variables. An case study was conducted to evaluate the performance of city bus transport companies in Taipei, Taiwan. Results showed the superiority of the proposed DFDEA model by comparing the results with static models.

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A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches

RAIRO - Operations Research ◽

10.1051/ro/2018019 ◽

2018 ◽

Vol 52 (4-5) ◽

pp. 1445-1463 ◽

Cited By ~ 7

Author(s):

Pejman Peykani ◽

Emran Mohammadi ◽

Mir Saman Pishvaee ◽

Mohsen Rostamy-Malkhalifeh ◽

Armin Jabbarzadeh

Keyword(s):

Data Envelopment Analysis ◽

Epistemic Uncertainty ◽

Maximum Efficiency ◽

Programming Approach ◽

Data Envelopment ◽

Fuzzy Data ◽

Fuzzy Measures ◽

Fuzzy Data Envelopment Analysis ◽

Possibilistic Programming ◽

Fuzzy Dea

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.

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Fuzzy Data Envelopment Analysis Models with R Codes

Data Envelopment Analysis with R - Studies in Fuzziness and Soft Computing ◽

10.1007/978-3-030-24277-0_5 ◽

2019 ◽

pp. 163-236

Author(s):

Farhad Hosseinzadeh Lotfi ◽

Ali Ebrahimnejad ◽

Mohsen Vaez-Ghasemi ◽

Zohreh Moghaddas

Keyword(s):

Data Envelopment Analysis ◽

Data Envelopment ◽

Fuzzy Data ◽

Fuzzy Data Envelopment Analysis ◽

Analysis Models

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Application of Fuzzy Data Envelopment Analysis in Decision Making

International Journal of Computer Applications ◽

10.5120/ijca2019919118 ◽

2019 ◽

Vol 178 (29) ◽

pp. 16-20

Author(s):

Akhilesh Kumar

Keyword(s):

Decision Making ◽

Data Envelopment Analysis ◽

Data Envelopment ◽

Fuzzy Data ◽

Fuzzy Data Envelopment Analysis

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An input relaxation measure of efficiency in fuzzy data envelopment analysis (FDEA)

Journal of Intelligent & Fuzzy Systems ◽

10.3233/ifs-2010-0468 ◽

2010 ◽

Vol 21 (6) ◽

pp. 395-403 ◽

Cited By ~ 1

Author(s):

M. Khodabakhshi ◽

Mona Hejrizadeh

Keyword(s):

Data Envelopment Analysis ◽

Data Envelopment ◽

Fuzzy Data ◽

Fuzzy Data Envelopment Analysis

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An Input-Output Orientation Model for Estimating Most Productive Scale Size in Fuzzy Data Envelopment Analysis

Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery - Advances in Intelligent Systems and Computing ◽

10.1007/978-3-030-70665-4_81 ◽

2021 ◽

pp. 750-760

Author(s):

Mingqiang Meng ◽

Lihong Liu

Keyword(s):

Data Envelopment Analysis ◽

Data Envelopment ◽

Fuzzy Data ◽

Input Output ◽

Orientation Model ◽

Scale Size ◽

Fuzzy Data Envelopment Analysis ◽

Most Productive Scale Size

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

Complex & Intelligent Systems ◽

10.1007/s40747-020-00211-x ◽

2020 ◽

Author(s):

Ali Ebrahimnejad ◽

Naser Amani

Keyword(s):

Data Envelopment Analysis ◽

Data Envelopment ◽

Undesirable Outputs ◽

New Approach ◽

Novel Approach ◽

Fuzzy Data Envelopment Analysis ◽

Relative Closeness ◽

Fuzzy Ideal ◽

Ideal Points ◽

Fuzzy Dea

Abstract 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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