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

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 384 ◽  
Author(s):  
Ali Namakin ◽  
Seyyed Najafi ◽  
Mohammad Fallah ◽  
Mehrdad Javadi
Keyword(s):  
Data Envelopment Analysis ◽  
Simple Structure ◽  
Data Envelopment ◽  
Imprecise Data ◽  
New Approach ◽  
Fuzzy Data Envelopment Analysis ◽  
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.

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

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.

DATA ENVELOPMENT ANALYSIS WITH IMPRECISE DATA: AN APPLICATION OF TAIWAN MACHINERY FIRMS

2005 ◽  
Vol 13 (02) ◽  
pp. 225-240 ◽  
Author(s):  
CHIANG KAO ◽  
SHIANG-TAI LIU
Keyword(s):  
Data Envelopment Analysis ◽  
Production Management ◽  
Fuzzy Numbers ◽  
Major Influence ◽  
Data Envelopment ◽  
Fuzzy Data ◽  
Imprecise Data ◽  
Fuzzy Data Envelopment Analysis ◽  
Automation Technology ◽  
Technology Level

Technology and management are two broad categories of factors that have major influence on the productivity of manufacturing firms. The ratio of the actual productivity of a firm to its maximal productivity is a measure of efficiency. Since the automation technology level and production management achievement of a firm cannot be measured precisely, a fuzzy data envelopment analysis (FDEA) model is applied to calculate the efficiency scores of a sample of machinery firms in Taiwan. Different from the conventional crisp DEA, the efficiency scores calculated from the FDEA model are fuzzy numbers, in that ranges of values at different possibility levels rather than a single crisp value are provided. When the observations are fuzzy in nature, the FDEA methodology avoids the top management from being over-confident with the results as opposed to that of using the conventional DEA methodology by simplifying the fuzzy observations to crisp values.

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

2013 ◽  
Vol 21 (01) ◽  
pp. 29-54 ◽  
Author(s):  
SABER SAATI ◽  
ADEL HATAMI-MARBINI ◽  
MADJID TAVANA ◽  
PER J. AGRELL
Keyword(s):  
Data Envelopment Analysis ◽  
Parametric Method ◽  
Data Envelopment ◽  
Output Data ◽  
Fuzzy Environment ◽  
Input And Output ◽  
Fuzzy Data Envelopment Analysis ◽  
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.

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

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 Analysis ◽  
Data Envelopment ◽  
Fuzzy Data ◽  
Fuzzy Approach ◽  
Discrimination Power ◽  
Sbm Model ◽  
Fuzzy Data Envelopment Analysis ◽  
Dea Models ◽  
Α Level ◽  
Fuzzy Dea

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.

Generalized Fuzzy Sample DEA Model and its Application in the Evaluation of Projects

2011 ◽  
Vol 63-64 ◽  
pp. 407-411
Author(s):  
Ren Mu ◽  
Zhan Xin Ma ◽  
Wei Cui ◽  
Yun Morigen Wu
Keyword(s):  
Decision Making ◽  
Data Envelopment Analysis ◽  
Data Envelopment Analysis Model ◽  
Data Envelopment ◽  
Input Output ◽  
Output Data ◽  
Dea Model ◽  
Decision Making Unit ◽  
Fuzzy Input ◽  
Fuzzy Dea

Evaluating the performance of activities or organizations by traditional data envelopment analysis model requires crisp input/output data. However, in real-world problems inputs and outputs are often with some fuzziness. To evaluate DMU with fuzzy input/output data, researchers provided fuzzy data envelopment analysis (FDEA) model and proposed related evaluating method. But up to now, we still cannot evaluate a fuzzy sample decision making unit (SDMU) for FDEA model. So this paper proposes a generalized fuzzy DEA model which can evaluate a sample decision making unit and a numerical experiment is used to illustrate this model.

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

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1445-1463 ◽  
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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