Fuzzy Data Envelopment Analysis Model Research Articles

A Malmquist fuzzy data envelopment analysis model for performance evaluation of rural healthcare systems

The primary purpose of this article is to measure the relative efficiency and productivity change over time in rural healthcare systems in the presence of fuzzy data. First, a novel ranking function based on the lower and upper bounds of alpha-cut of the trapezoidal fuzzy numbers (TrFNs) is proposed to compare the TrFNs. The suggested ranking technique is used to construct the fuzzy data envelopment analysis (FDEA), Malmquist fuzzy DEA (Mal-FDEA), and undesirable Malmquist fuzzy DEA (UN-Mal-FDEA ) models. The proposed models evaluate the efficiency and productivity of decision-making units (DMUs) when the input and output data are given in the form of TrFNs. In addition, a case study of the rural healthcare system in a developing country has been considered to demonstrate the applicability of the developed models. The work considers number of sub-centers (SCs), the number of primary health centers (PHCs), the number of community health centers (CHCs), nursing Staff at PHCs, an auxiliary nurse and midwives (ANM) at SCs, doctors at PHCs, pharmacists at PHCs, laboratory technicians at PHCs, radiographers at CHCs, and specialists at CHCs as input parameters and average population covered by CHCs, average village covered by CHCs, number of patients, and infant mortality rates as output parameters to analyze the performance of the rural healthcare systems. We show the UN-Mal-FDEA model has a higher production value than the Mal-FDEA model. The results of our proposed models enable us to recognize inefficiencies that states may rectify without compromising healthcare quality.

A new intuitionistic fuzzy scheme of data envelopment analysis for evaluating rural comprehensive health service centers

In this study, the classical CCR-IO DEA model (an input-oriented form of the DEA model of Charnes, Cooper, and Rhodes [24] is extended to an intuitionistic fuzzy environment. For this aim, the trapezoidal intuitionistic fuzzy numbers are used to show the values of inputs and outputs. An intuitionistic fuzzy number is characterized by membership, non-membership, and hesitancy degrees. Therefore, such type of fuzzy numbers is more complete and contains more information to reflect a fuzzy type of uncertainty comparing to the conventional fuzzy values. In order to solve the proposed intuitionistic fuzzy CCR-IO model, for the first time a possibility-based approach is developed for the intuitionistic fuzzy DEA models. In this approach for the first time the ME measure of fuzzy events is extended to intuitionistic fuzzy DEA models, therefore, some new definitions and propositions are presented and clarified. This measure is more flexible and effective comparing to the other measures such as credibility, necessity, and possibility measures. A case study from the health care sector of Iran is considered to evaluate the proposed solution approach numerically. The case study is solved under different scenarios, a full sensitivity analysis is performed, and finally some useful managerial insights are presented. In addition, the results of the proposed intuitionistic CCR-IO model are compared to the classical models of the literature.

A Novel Pythagorean Approach Based Sine-Shaped Fuzzy Data Envelopment Analysis Model: An Assessment of Indian Public Sector Banks

A Novel Pythagorean Approach Based Sine-Shaped Fuzzy Data Envelopment Analysis Model: An Assessment of Indian Public Sector Banks

Hierarchical fuzzy DEA model with double frontiers combined with TOPSIS technique: application on mobile money agents locations

Hierarchical fuzzy DEA model with double frontiers combined with TOPSIS technique: application on mobile money agents locations

Measuring the eco-efficiency of municipal solid waste service: A fuzzy DEA model for handling missing data

In the last decades, evaluating the performance of municipal solid waste (MSW) service has attracted the interest of scholars and policymakers worldwide. This study adopts a generalized directional distance function (GDDF) data envelopment analysis (DEA) model to measure the eco-efficiency of 94 Apulian municipalities providing MSW service over 2019–2021. The model uses the α-cut method to handle missing data in a fuzzy DEA environment. During the period covered by the research, on average, the MSW eco-efficiency was between 0.825 and 0.879. The MSW separate collection rate is the only factor significantly affecting the MSW eco-efficiency.

The ‘Healthcare Access and Quality Index’ revisited: A fuzzy data envelopment analysis approach

Nowadays, health systems comprise a series of resources structured to provide healthcare services to meet our health needs. However, premature deaths still occur. To quantify and understand personal healthcare conditions affecting such amenable mortality, the Healthcare Access and Quality Index (HAQI) was put forward, evaluating 195 countries and territories since 1990. Nevertheless, the literature acknowledges a series of limitations of this framework, such as the drawbacks of using principal component analysis to aggregate individual indicators, the absence of control for financing and environmental conditions, and the presence of a substantial degree of data uncertainty. Accordingly, we propose a methodological alternative to the computation of the HAQI using a novel fuzzy Data Envelopment Analysis model to handle the aforementioned shortcomings. We also propose its extension towards the quantification of efficiency (E-HAQI) – in the sense of value for money – by incorporating financial aspects as modelling inputs. This way, we contribute with innovative modelling approaches that can also deal with the high degree of data uncertainty. Furthermore, in a second-stage analysis, the impact of key exogenous factors on healthcare access and quality is assessed via non-parametric hypothesis testing. Our results show positive and significant correlations of both the revisited HAQI and E-HAQI with the original HAQI 2016 dataset. They also reveal a better use of resources by European and Oceanian countries and territories than by Sub-Saharan African ones. Concerning contextual determinants, socio-demographic development, human development, and the type of health system were found to be statistically significant drivers of healthcare access and quality efficiency.

A novel technique for solving intuitionistic fuzzy DEA model: an application in Indian agriculture sector

Fuzzy DEA is a performance measurement tool that is used to assess the performance of DMUs in highly uncertain environments. In this article, the Intuitionistic fuzzy DEA (IFDEA) model is proposed based on the triangular intuitionistic fuzzy numbers (TIFNs). The weighted Possibility mean for TIFN is used to compare and rank the TIFN. The weighted possibility mean approach is proposed to solve the IFDEA model, and the IFDEA model is converted into its equivalent crisp DEA model to assess the relative efficiencies of the DMUs. One advantage of the proposed approach is that the attitude of the decision-maker is considered while measuring the efficiency of the DMUs. The weight or risk factor delta in [0,1] indicates whether the decision-maker is a risk-taker, neutral, or adverse. The crisp DEA model is a LP problem that is solved by using an existing LP method with different risk factors to determine the efficiency score of the DMUs. The DMUs are ranked based on the overall efficiency score of the DMUs, which is the arithmetic mean of the efficiency scores of the DMUs with different risk factors. Two numerical examples are given here to demonstrate the validity and applicability of the proposed technique and to compare the performance of the DMUs in the proposed approach with the exciting ranking approach and the expected value approach. A case study on the agriculture sector has been conducted in order to evaluate the agricultural performance of Indian states using the IFDEA model. According to the results of the IFDEA model, 15 (53.57%) out of the 28 Indian states were found to be efficient.

Fully fuzzy DEA: a novel additive slacks-based measure model

AbstractThe subject of assessing the relative efficiency of Decision-Making Units (DMUs) has been explored extensively in the literature on Data Envelopment Analysis (DEA). While typical DEA models require exact and conclusive data, the observed values of the inputs and outputs in real-world problems may be inaccurate or ambiguous. This paper presents a novel fully fuzzy DEA (FFDEA) model based on the additive slacks-based measure (ASBM). FFDEA models imply that all inputs, outputs, and variables, are fuzzy. It is demonstrated how fuzzy ranking and fuzzy arithmetic approaches can be used to handle the trapezoidal fuzzy number assumptions. To solve the fuzzy ASBM model under variable returns-to-scale assumptions, we proposed two different methods, first method use of lexicographic method for solving multi-objective linear programming (MOLP) approach, which provides an efficiency measure and a fuzzy goal operating point for each DMU under assessment. In alternative method, we convert the fuzzy linear fractional programming problems to an equivalent MOLP problem. A case study is provided to illustrate the applicability of the proposed approach for selecting sustainable suppliers, we compare the results with other fuzzy DEA approaches, while shedding light on future research venues.

An Economic Mathematical Fuzzy Model for Data Envelopment Analysis

Performance assessment is a central to the management process in any type of organization. In addition, making rational economical decisions to improve organizational performance is a daunting task, as any organization is typically a multi-faceted entity which rely on complex systems that use uncertain information. Data envelopment analysis (DEA) is a powerful quantitative tool that makes use of multiple inputs and outputs to obtain useful information about the performance and efficiency of an organization. In many real-life applications, observations are usually fuzzy in nature. Therefore, DEA efficiency measurement may be sensitive to such variations. The purpose of this study is to develop a unified economical fuzzy DEA model that handles variables of different natures (vague and deterministic) independently and can be adapted to both input- and output-oriented problems, whether it is constant/variable return to scale. To handle fuzzy variables specially the economic variables in the model, the -cut approach was adopted. The model implementation is demonstrated through an illustrative case study. Managers will be able to use this model to identify and remedy underperformance, as well as to design regulations that aim to encourage efficiency and ensure that consumers benefit from the resulting efficiency gains.

Common-weights fuzzy DEA model in the presence of undesirable outputs with ideal and anti-ideal points: development and prospects

AbstractIn the literature, fuzzy arithmetic approach has been used for solving fuzzy data envelopment analysis (DEA) model in the presence of undesirable outputs by use of ideal and anti-ideal decision-making units (DMUs). In order to obtain the best and the worst fuzzy efficiencies, such an approach allows each DMU to choose the most favorable weights via optimizing its own evaluation that needs to solve various mathematical models. On the one hand, solving one mathematical model to find the best fuzzy efficiency and solving another mathematical model to find the worst fuzzy efficiency for each DMU increase the computational complexity significantly. On the other hand, the fully flexibility of weights leads to the different set of weights that may not be desirable. This paper proposes a common-weight method from two optimistic and pessimistic perspectives in fuzzy environment to determine the common sets of weights (CWS) to compute the best and the worst fuzzy efficiencies of all DMUs. The advantages of using common-weight DEA method based upon fuzzy arithmetic approach are reduction of the computational complexities and evaluation of equitably the best and the worst fuzzy efficiencies on the same base. The proposed approach first solves one linear programming model to compute each of the best and the worst fuzzy efficiencies of all DMUS, and then combines them to find a relative closeness index for the overall assessment. The developed approach is illustrated by a numerical example form the literature and the obtained results are compared with those from the existing ones.

Investigating the ability of fuzzy and robust DEA models to apply uncertainty conditions: an application for date palm producers

Investigating the ability of fuzzy and robust DEA models to apply uncertainty conditions: an application for date palm producers

Development of Bi-Objective Fuzzy Data Envelopment Analysis Model to Measure the Efficiencies of Decision-Making Units

The proposed bi-objective fuzzy data envelopment analysis (BOFDEA) model is a new approach to assess the performance efficiency of decision-making units (DMUs) in uncertain environments using α-cuts. The model is based on fuzzy data envelopment analysis (FDEA) and considers two objectives, and a solution method and ranking system are provided. Generally, the efficiency score obtained for a DMU using the α-cut approach is an interval. Intervals are partially ordered sets, due to which ranking intervals is a challenging task. The proposed BOFDEA model with α-cuts provides the efficiency of DMUs in the crisp form, not in the form of intervals. Due to this, ranking DMUs with the proposed method’s help becomes very easy and less computationally. The proposed model has been validated through numerical examples, and a real-world application in the education sector has been shown to demonstrate its practicality.

Evaluating the Quality of Engineering Translator Training Based on the DEA Model

This paper adopts the DEA model to conduct in-depth research and analysis on the evaluation of the quality training of engineering English translation talents. The BIM application performance of nine engineering projects is empirically analyzed, including slack value analysis, correlation validity analysis, and BIM application performance path optimization. The nine cases have an unreasonable allocation of resources invested in BIM application in the early stage so that the performance path optimization is carried out to find out the key paths for the reallocation of resources. Further analysis of BIM application performance improvement strategies, including strengthening the training of BIM application professionals. The fuzzy two-stage DEA model with adjustable fuzzy opportunity constraint constructed for the situation where both intermediate and final processes have non-desired outputs. First, the additive efficiency decomposition model in the exact number environment is extended to the non-desired output situation. Second, the generalized fuzzy measure and opportunity constraint planning are applied to further extend the model to a non-expected output fuzzy DEA model, and a two-stage DEA model with adjustable fuzzy opportunity constraints is constructed. There are still some differences between the two. Strengthening practice is the general trend of current curriculum reform in our country. Finally, the proposed model is applied to the evaluation problem of quality training of engineering English translators. The adjustable fuzzy opportunity-constrained DEA model proposed in this paper can effectively evaluate the efficiency of real production and operation activities. The research results of this paper not only enrich the existing DEA model theoretical system but also have broad application prospects and values in practical problems. We provide a reasonable guarantee in terms of system and funding and pay attention to the follow-up communication with employers to strengthen the implementation of the influence of social forces on the quality evaluation of English teaching in higher education. To a certain extent, this study enriches the theoretical research on the quality evaluation of English translation talents’ quality training and can play a role in strengthening and improving the quality evaluation of translation talents’ quality training at the present stage.

Fund-based Activity of Indian Small Finance Banks: A Fuzzy DEA Approach

The objective of this article is to promote financial inclusion in the niche market for the less privileged class of the society by allowing small finance banks that are specialized in terms of activity with a regional focus and the target population. The present study makes an efficiency evaluation of the small finance banks operating in India for the period 2017–2020. In view of the smallness of the sample size, the study estimates efficiency, not by the conventional data envelopment analysis (DEA)-based point estimates. Instead, it estimates efficiency by applying the Guo–Tanaka fuzzy DEA model. In the second stage, efficiency is explained in terms of three contextual variables: return on asset, capital adequacy and net non-performing asset ratio. JEL Classifications: C61, D21, G21

Evaluation Method of Performance of Cross-Border e-Commerce System Based on Fuzzy DEA Model

Cross-border e-commerce trade is an important form of trade that is different from traditional international trade. Nowadays, cross-border e-commerce is more and more widely used in foreign trade activities. Cross-border e-commerce system has its own development constraints, such as the imperfection of cross-border e-commerce platforms, the security loopholes of cross-border payment, the slow development of supporting logistics, and the lag of policies, which will affect its development to varying degrees, thus affecting the performance of e-commerce enterprises in using cross-border e-commerce for foreign trade activities. Therefore, it is necessary to explore the factors of cross-border e-commerce system performance and compare the strength of various factors, which has certain theoretical and practical significance. Therefore, based on the analysis of performance data, this paper will establish a performance evaluation model for an e-commerce system, aiming at providing standards and a basis for performance evaluation of system performance. In order to continuously improve the accuracy of cross-border e-commerce performance evaluation and to achieve the accuracy of cross-border e-commerce evaluation and decision-making, a cross-border e-commerce system performance evaluation model based on the fuzzy DEA model is innovatively proposed. By combining the average analysis results of descriptive statistical data, the regression test is conducted on the performance evaluation samples of cross-border e-commerce systems. The fuzzy feature clustering method is used to classify and identify the performance of big data in the cross-border e-commerce system. According to the fusion results of cross-border e-commerce performance information, the principal component analysis and adaptive game decision are carried out, and the game decision model is established. Combined with the fuzzy DEA evaluation method, the performance of the cross-border e-commerce system can be quantified and evaluated. The F statistical analysis method is used to test the effectiveness of the performance evaluation of the cross-border e-commerce system. From the test results, it can be seen that the performance evaluation accuracy of the cross-border e-commerce system using this model is relatively high, and the confidence level is also relatively good. Finally, according to the conclusion of the study, the author puts forward the counter-measures for future research.

New Advances on Fuzzy Linear Programming Problem by Semi-Infinite Programming Approach

As we are faced with more uncertainty problems in the real world, it is necessary to ‎provide ‎models that can provide appropriate solutions for dealing with these issues. In this ‎study, we ‎ proposed a new approach to solving linear programming problem in the fuzzy ‎environment ‎based on solving ‎a related multi-objective model. This kind of problem can be ‎reduced to a ‎fuzzy linear semi-infinite programming problem. In this way, we present a new ‎mixed ‎Multi-Objective Linear Semi-Infinite Programming (MOLSIP) model to solve the ‎main ‎problem, furthermore, as a practical case, we consider a fuzzy Data Envelopment ‎Analysis ‎‎(DEA) model which is a concern to‎ an evaluation of the performance of Decision-‎Making ‎Units (DMUs) in uncertainty environment, The new models show the advantage of ‎our ‎method over the previous ones in terms of certainty. Finally, numerical examples ‎are ‎included to illustrate the suggested solution procedure.‎

Data Envelopment Analysis on the Context of Spherical Fuzzy Inputs and Outputs

In this study, Data Envelopment Analysis (DEA) models are improved by employing spherical fuzzy sets (SFSs), which is an extension of generalized fuzzy sets. SFSs were recently introduced as a novel type of fuzzy set that allows decision-makers to express their level of uncertainty directly. As a result, SFSs provide a more preferred domain for decision-makers. Fundamental Charnes-Cooper-Rhodes (CCR) model is discussed on the context of spherical trapezoidal fuzzy numbers (STrFNs), which consider each data value’s truth, indeterminacy, and falsehood degrees, and a unique solution technique is implemented. This method converts a spherical fuzzy DEA(SF-DEA) model into three pair of crisp DEA model, which may then be solved using one of many existing approaches. The largest optimal interval is determined for each DMU such that the efficiency score lies inside that interval. Furthermore, an example demonstrates this novel method and clearly explains the DMUs’ ranking technique.

Assessing most productive scale size with fuzzy stochastic data envelopment analysis

Classic data envelopment analysis (DEA) is a linear programming method for evaluating the relative efficiency of decision making units (DMUs) that uses multiple inputs to produce multiple outputs. In the classic DEA model inputs and outputs of DMUs are deterministic, while in the real world, are often fuzzy, random, or fuzzy-random. Many researchers have proposed different approaches to evaluate the relative efficiency with fuzzy and random data in DEA. In many studies, the most productive scale size (mpss) of decision making units has been estimated with fuzzy and random inputs and outputs. Also, the concept of fuzzy random variable is used in the DEA literature to describe events or occurrences in which fuzzy and random changes occur simultaneously. This paper has proposed the fuzzy stochastic DEA model to assess the most productive scale size of DMUs that produce multiple fuzzy random outputs using multiple fuzzy random inputs with respect to the possibility-probability constraints. For solving the fuzzy stochastic DEA model, we obtained a nonlinear deterministic equivalent for the probability constraints using chance constrained programming approaches (CCP). Then, using the possibility theory the possibilities of fuzzy events transformed to the deterministic equivalents with definite data. In the final section, the fuzzy stochastic DEA model, proposed model, has been used to evaluate the most productive scale size of sixteen Iranian hospitals with four fuzzy random inputs and two fuzzy random outputs with symmetrical triangular membership functions.

Evaluating the Efficiency of Decision Making Units in Fuzzy two-stage DEA Models

Data envelopment analysis (DEA) is an optimization method to assess the efficiency of decision-making units with multiple-inputs/multiple-outputs assumption. Most real-life issues contain more than one stage unit which needs multiple-stage data envelopment analysis models to be solved. Moreover, the inputs and outputs of the units are rarely measured accurately in real-life problems, hence fuzzy data envelopment analysis approaches can be significantly helpful in calculating efficiency scores. In this study, an approach for evaluating the performance of decision-making units (DMUs) in fuzzy two-stage DEA models is developed. The developed model is a parametric program based on alpha-cuts. The dependence on alpha allows the manager to compare and rank DMUs based on his/her degree of certainty and after the selection of alpha, our proposed model becomes linear. Furthermore, a theorem is proposed and proved for conventional multiplicative two-stage DEA models with the assumption of Variable Returns to Scale. This theorem can be used to evaluate the correctness of the results. Finally, by two illustrative examples, the ability of the proposed approach to solve fuzzy two-stage DEA models is shown, and the obtained results are compared to that of some other methods in this field.

Constructing fuzzy composite indicators to support water policy entrepreneurship

Composite indicators play a very useful role in supporting international policy entrepreneurship, helping to inform decision-making processes and to address conflicts between countries. In this paper we present a Fuzzy Data Envelopment Analysis (Fuzzy-DEA) model to construct composite indicators based on time series under the Pressure-State-Response (PSR) approach in order to evaluate water security in 10 European water security hotspots. First, we identified nine indicators within the PSR framework. Second, we aggregated the indicators in each PSR set using a Fuzzy-DEA model. Finally, we compared the PSR results under pessimistic, optimistic and neutral scenarios. Results show that, overall, Bulgaria achieved the best pressure, state and response performance. In terms of responses, Spain registered the best performance after Bulgaria, despite the fact that it suffers from the highest pressures of all the analyzed countries. Estonia achieved the best state performance in all three scenarios, but worse results in responses than Bulgaria and Spain. Cyprus and Belgium registered the highest variability for pressures, Spain for state and Portugal for responses.The model was able to pinpoint the problems that political strategies and urgent actions should seek to tackle, while providing information regarding the variability of the indicators over time.