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

Data Envelopment ◽

Undesirable Outputs ◽

New Approach ◽

Novel Approach ◽

Relative Closeness ◽

Fuzzy Ideal ◽

Ideal Points ◽

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.

A New Evaluation for Solving the Fully Fuzzy Data Envelopment Analysis with Z-Numbers

Symmetry ◽

10.3390/sym10090384 ◽

2018 ◽

Vol 10 (9) ◽

pp. 384 ◽

Cited By ~ 4

Author(s):

Ali Namakin ◽

Seyyed Najafi ◽

Mohammad Fallah ◽

Mehrdad Javadi

Keyword(s):

Simple Structure ◽

Data Envelopment ◽

Imprecise Data ◽

New Approach ◽

Fuzzy Input ◽

Fully Fuzzy Dea ◽

Fuzzy Dea ◽

Real World Problems

There are numerous models for solving the efficiency evaluation in data envelopment analysis (DEA) with fuzzy input and output data. However, because of the limitation of those strategies, they cannot be implemented for solving fully fuzzy DEA (FFDEA). Furthermore, in real-world problems with imprecise data, fuzziness is not sufficient to consider, and the reliability of the information is also very vital. To overcome these flaws, this paper presented a new method for solving the fully fuzzy DEA model where all parameters are Z-numbers. The new approach is primarily based on crisp linear programming and has a simple structure. Moreover, it is proved that the only existing method to solve FFDEA with Z-numbers is not valid. An example is also presented to illustrate the efficiency of our proposed method and provide an explanation for the content of the paper.

A FUZZY DATA ENVELOPMENT ANALYSIS FOR CLUSTERING OPERATING UNITS WITH IMPRECISE DATA

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488513500037 ◽

2013 ◽

Vol 21 (01) ◽

pp. 29-54 ◽

Cited By ~ 10

Author(s):

SABER SAATI ◽

ADEL HATAMI-MARBINI ◽

MADJID TAVANA ◽

PER J. AGRELL

Keyword(s):

Parametric Method ◽

Data Envelopment ◽

Output Data ◽

Fuzzy Environment ◽

Input And Output ◽

Human Decision ◽

Fuzzy Dea ◽

Operating Units

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiency of peer operating units that employ multiple inputs to produce multiple outputs. Several DEA methods have been proposed for clustering operating units. However, to the best of our knowledge, the existing methods in the literature do not simultaneously consider the priority between the clusters (classes) and the priority between the operating units in each cluster. Moreover, while crisp input and output data are indispensable in traditional DEA, real-world production processes may involve imprecise or ambiguous input and output data. Fuzzy set theory has been widely used to formalize and represent the impreciseness and ambiguity inherent in human decision-making. In this paper, we propose a new fuzzy DEA method for clustering operating units in a fuzzy environment by considering the priority between the clusters and the priority between the operating units in each cluster simultaneously. A numerical example and a case study for the Jet Ski purchasing decision by the Florida Border Patrol are presented to illustrate the efficacy and the applicability of the proposed method.

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

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v15i2.2051 ◽

2019 ◽

pp. 481-501

Author(s):

Qaiser Farooq Dar ◽

Ahn Young Hyo ◽

Gulbadian Farooq Dar ◽

Shariq Ahmad Bhat ◽

Arif Muhammad Tali ◽

...

Keyword(s):

Data Envelopment ◽

Fuzzy Data ◽

Fuzzy Approach ◽

Discrimination Power ◽

Sbm Model ◽

Dea Models ◽

Α Level ◽

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.

A New Approach to Solve Fuzzy Data Envelopment Analysis Model Based on Uncertainty

IEEE Access ◽

10.1109/access.2020.3022158 ◽

2020 ◽

Vol 8 ◽

pp. 167300-167307

Author(s):

Maryam Olfati ◽

Wenjun Yuan ◽

Asad Khan ◽

Seyed Hadi Nasseri

Keyword(s):

Data Envelopment Analysis Model ◽

Data Envelopment ◽

Fuzzy Data ◽

Analysis Model ◽

New Approach ◽

Model Based ◽

Fuzzy Data Envelopment Analysis

Ecological Evaluation of Industrial Parks Using a Comprehensive DEA and Inverted-DEA Model

Mathematical Problems in Engineering ◽

10.1155/2020/9397806 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Bingjiang Zhang ◽

Jinling Guo ◽

Zheng Wen ◽

Zhaoyao Li ◽

Ning Wang

Keyword(s):

Data Envelopment ◽

Undesirable Outputs ◽

Discrimination Power ◽

New Approach ◽

Discrimination Ability ◽

Industrial Parks ◽

Overall Evaluation ◽

Score Method ◽

Desirable And Undesirable Outputs

Data envelopment analysis (DEA) and inverted data envelopment analysis (inverted-DEA) are used so that the desirable and undesirable outputs of decision-making units (DMUs) exist simultaneously. We developed a new approach based on the concept of utilizing both DEA and inverted-DEA to enhance the discrimination power of DMUs with undesirable outputs. DMUs are ranked by the Z-score method and classified based on the efficiency scores of DEA and inverted-DEA. Then, the characteristics of the DMUs are analyzed based on the classification result. This paper performs an efficiency evaluation of 21 industrial parks in China in 2017 using this new approach. The overall evaluation results indicate that the proposed new approach increases the discrimination ability in this empirical study.

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):

Epistemic Uncertainty ◽

Maximum Efficiency ◽

Programming Approach ◽

Data Envelopment ◽

Fuzzy Data ◽

Fuzzy Measures ◽

Possibilistic Programming ◽

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.

Data Envelopment Analysis with Common Weights in a Fuzzy Environment

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488517500386 ◽

2017 ◽

Vol 25 (06) ◽

pp. 897-915 ◽

Cited By ~ 1

Author(s):

Cheng-Kai Hu ◽

Fung-Bao Liu ◽

Cheng-Feng Hu

Keyword(s):

Data Envelopment Analysis Model ◽

Data Envelopment ◽

Analysis Model ◽

Fuzzy Environment ◽

Order Preference ◽

Entropic Regularization ◽

Common Weight ◽

This work considers providing a common base for measuring the relative efficiency of a group of homogeneous decision making units in a fuzzy environment. The principle of compromise of the technique for order preference by similarity ideal solution is employed for solving the data envelopment analysis model with fuzzy objectives and constraints. An algorithm with the entropic regularization implementation for finding the compromise solution of the fuzzy data envelopment analysis model is developed. An illustrative example verifying the idea of this paper is provided. The contribution of this work is represented by the improvement of the discriminatory power of the fuzzy DEA, gained through the common weight evaluation.

Relative Efficiency of Decision Making Units Producing Both Desirable and Undesirable Outputs: A Case of Textile Processing Units in Pakistan.

The Pakistan Development Review ◽

10.30541/v50i4iipp.685-698 ◽

2011 ◽

Vol 50 (4II) ◽

pp. 685-698

Author(s):

Samina Khalil

Keyword(s):

Decision Making ◽

Relative Efficiency ◽

Value Added ◽

Data Envelopment ◽

Undesirable Outputs ◽

Textile Processing ◽

Decision Making Unit ◽

Desirable And Undesirable Outputs ◽

Decision Making Units

This paper aims at measuring the relative efficiency of the most polluting industry in terms of water pollution in Pakistan. The textile processing is country‘s leading sub sector in textile manufacturing with regard to value added production, export, employment, and foreign exchange earnings. The data envelopment analysis technique is employed to estimate the relative efficiency of decision making units that uses several inputs to produce desirable and undesirable outputs. The efficiency scores of all manufacturing units exhibit the environmental consciousness of few producers is which may be due to state regulations to control pollution but overall the situation is far from satisfactory. Effective measures and instruments are still needed to check the rising pollution levels in water resources discharged by textile processing industry of the country. JEL classification: L67, Q53 Keywords: Data Envelopment Analysis (DEA), Decision Making Unit (DMU), Relative Efficiency, Undesirable Output

Fuzzy preference programming formulation in data envelopment analysis for university department evaluation

Journal of Modelling in Management ◽

10.1108/jm2-08-2020-0205 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Dyanne Brendalyn Mirasol-Cavero ◽

Lanndon Ocampo

Keyword(s):

Real Life ◽

The Philippines ◽

Data Envelopment ◽

Data Accessibility ◽

Content Type ◽

Proposed Model ◽

University Department ◽

Fuzzy Dea ◽

Fuzzy Preference

Purpose University department efficiency evaluation is a performance assessment on how departments use their resources to attain their goals. The most widely used tool in measuring the efficiency of academic departments in data envelopment analysis (DEA) deals with crisp data, which may be, often, imprecise, vague, missing or predicted. Current literature offers various approaches to addressing these uncertainties by introducing fuzzy set theory within the basic DEA framework. However, current fuzzy DEA approaches fail to handle missing data, particularly in output values, which are prevalent in real-life evaluation. Thus, this study aims to augment these limitations by offering a fuzzy DEA variation. Design/methodology/approach This paper proposes a more flexible approach by introducing the fuzzy preference programming – DEA (FPP-DEA), where the outputs are expressed as fuzzy numbers and the inputs are conveyed in their actual crisp values. A case study in one of the top higher education institutions in the Philippines was conducted to elucidate the proposed FPP-DEA with fuzzy outputs. Findings Due to its high discriminating power, the proposed model is more constricted in reporting the efficiency scores such that there are lesser reported efficient departments. Although the proposed model can still calculate efficiency no matter how much missing and unavailable, and uncertain data, more comprehensive data accessibility would return an accurate and precise efficiency score. Originality/value This study offers a fuzzy DEA formulation via FPP, which can handle missing, unavailable and imprecise data for output values.

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 ◽

Fuzzy Data ◽

Analysis Models