Fuzzy Data Envelopment Analysis Approach Research Articles

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.

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.

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

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.

Neurotic Fuzzy-Data-Envelopment Analysis to Forecast Efficiency of Bank Branches

In this study the prediction of efficiency of four different Bank Branches have been done by using Neurotic Fuzzy Data Envelopment Analysis approach. In the first stage of the study, Artificial Neural Network (ANN) model has been modelled and trained using the last five years data. The data belonging any year has been taken as input of ANN, next year data has been defined as output of ANN. Fuzzyfication process has been applied to obtained predictions based on asking managers of bank branches, after Fuzzy Data Envelopment Analysis process has been applied to fuzzy values. As a result, the bank branches parameters belonging to 2021 year have been obtained. The efficiency of 2021 for bank branches have been calculated based on Fuzzy Data Envelopment Analysis (FDEA).

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

PurposeUniversity 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/approachThis 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.FindingsDue 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/valueThis study offers a fuzzy DEA formulation via FPP, which can handle missing, unavailable and imprecise data for output values.

Efficiency Analysis with Educational Data: How to Deal with Plausible Values from International Large-Scale Assessments

International large-scale assessments (ILSAs) provide several measures as a representation of educational outcomes, the so-called plausible values, which are frequently interpreted as a representation of the ability range of students. In this paper, we focus on how this information should be incorporated into the estimation of efficiency measures of student or school performance using data envelopment analysis (DEA). Thus far, previous studies that have adopted this approach using data from ILSAs have used only one of the available plausible values or an average of all of them. We propose an approach based on the fuzzy DEA, which allows us to consider the whole distribution of results as a proxy of student abilities. To assess the extent to which our proposal offers similar results to those obtained in previous studies, we provide an empirical example using PISA data from 2015. Our results suggest that the performance measures estimated using the fuzzy DEA approach are strongly correlated with measures calculated using just one plausible value or an average measure. Therefore, we conclude that the studies that decide upon using one of these options do not seem to be making a significant error in their estimates.

Developing a new integrated artificial immune system and fuzzy non-discretionary DEA approach

As a useful performance evaluation and decision-making tool, data envelopment analysis (DEA) has been proven to be an excellent data-oriented efficiency analysis method when there are multiple inputs and outputs. However, when working with large datasets, DEA requires more time to solve and calculate the optimal values for each decision-making unit (DMU). To close this methodological gap, this study proposes a new integrated fuzzy nondiscretionary DEA (FNDEA) model and artificial immune system (AIS) to predict and find the optimal values of DMUs. In so doing, we first modify an FNDEA model to classify the set of all DMUs into efficient and inefficient, and immune system (AIS) is used to predict and find the optimal values of DMUs. Then, a modified fuzzy nondiscretionary additive DEA model, which is designed as a middle chain, is used for sensitivity analysis of inefficient DMUs to determine their target outputs, which are called antigens. Finally, we try to reduce the distance between these two steps in order to predict the optimal values (with nearest distance to antigens) of inefficient DMUs and improve their efficiency by using a combined AIS and FNDEA model called the FNDEA–AIS approach. To illustrate the advantages of the proposed FNDEA–AIS approach, a dataset from 24 Iranian forest management units is collected; the results indicated that our new FNDEA–AIS approach (in comparison with other well-established performance prediction techniques) exhibits better convergent validity and high correlation with low error rate to predict optimal values of inefficient DMUs. The main conclusion is that our new applied method, developed for the first time herein, provides a suitable improvement over previously developed methods, such as artificial neural networks (ANNs), to detect inefficiency and to improve the overall performance when analyzing different types of real-life problems.

Fuzzy Type-II Resource Allocation and Target Setting in Data Envelopment Analysis: A Real Case of Gas Refineries

Data envelopment analysis (DEA) is a linear programming method to measure the relative efficiency of a set of decision-making units (DMUs) with multiple inputs and outputs. Some DEA models are used to allocate resources and to set targets. Previous studies in resource allocation and target setting have used deterministic data; however, in real problems resources and targets are not deterministic. In this paper, a type-II fuzzy DEA approach is developed for resource allocation and target setting. A numerical example and a real case study including 11 gas refineries with two inputs and three outputs are provided to illustrate the performance of the proposed approach. The results demonstrate that the proposed method efficiently allocates resources and sets targets in presence of uncertainty. Sensitivity analysis is accomplished based on the variation of the value of targets and resources and the variation of the footprint of uncertainty (FOU) of resources and targets.

Fuzzy Ranking Network DEA with General Structure

This paper extends two fuzzy ranking data envelopment analysis (DEA) approaches to the case of general networks of processes. The first approach provides an efficiency score for each possibility level which requires solving one linear program for each possibility level. The second approach is even simpler and provides an overall efficiency score solving just one linear program. The proposed approaches are tested on two datasets from the literature and compared with other fuzzy network DEA approaches. The results show that the two methods provide very highly correlated efficiency estimates which are also consistent with those of other fuzzy network DEA approaches.

Performance evaluation of yarn raw materials supplier using fuzzy data envelopment analysis approach (case study Batik Fabric Company in Sleman)

Evaluating supplier performance by measuring supplier performance is an important thing by the company to optimize costs and time. This study aims to evaluate supplier performance and determine the best supplier based on predetermined criteria. This research was conducted on Batic Fabric company by taking research object suppliers of raw material for 40 CD and 50 CM yarn. This study used 4 criteria and 3 month period data. Evaluation of supplier performance using the Fuzzy Data Envelopment Analysis (DEA) approach, the Fuzzy method is used to carry out linguistic assessments, while for the assessment efficiency is used by the DEA method. The result analysis was concluded that the efficient suppliers for 40 CD yarns were suppliers PTX1, PMT1 and AG1. PMT1 is the best supplier which has the highest super efficiency value of 10.01565 while the 2nd rank is occupied by the PTX1 supplier with a super efficiency value of 1.633666 and the third rank is AG1 supplier with a super efficiency value of 1,488659 and other suppliers are inefficient: PMT1, SC1, PDT1 and AR1. For 50 CM yarn, the best supplier is PTX2 which has an efficiency value of 1, while other suppliers are inefficient: PMT2, DLT2, and DLR2.

An adjustable fuzzy chance-constrained network DEA approach with application to ranking investment firms

This paper presents a novel approach for performance appraisal and ranking of decision-making units (DMUs) with two-stage network structure in the presence of imprecise and vague data. In order to achieve this goal, two-stage data envelopment analysis (DEA) model, adjustable possibilistic programming (APP), and chance-constrained programming (CCP) are applied to propose the new fuzzy network data envelopment analysis (FNDEA) approach. The main advantages of the proposed FNDEA approach can be summarized as follows: linearity of the proposed FNDEA models, unique efficiency decomposing under ambiguity, capability to extending for other network structures. Moreover, FNDEA approach can be applied for ranking of two-stage DMUs under fuzzy environment in three stages: 1) solving the proposed FNDEA model for all optimistic-pessimistic viewpoints and confidence levels, 2) then plotting the results and drawing the surface of all efficiency scores, 3) and finally calculate the volume of the three-dimensional shape in below the efficiency surface. This volume can be as ranking criterion. Remarkably, the presented fuzzy network DEA approach is implemented for performance appraisal and ranking of investment firms (IFs) with two-stage processes including operational and portfolio management process. Illustrative results of the real-life case study show that the proposed approach is effective and practically very useful.

A fuzzy DEA slacks-based approach

This paper deals with the problem of efficiency 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 inefficiency proportions, a well-known slacks-based additive inefficiency measure, is considered. The proposed approach also provides fuzzy input and output targets. Computational experiences and comparison with other fuzzy DEA approaches are reported.

Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem

In this paper, a transportation problem (TP) with fuzzy costs in the presence of multiple and conflicting objectives is investigated. In fact, a fuzzy data envelopment analysis (DEA) approach is proposed to solve the fuzzy multi-objective TP (FMOTP). To this end, each arc in FMOTP will be considered as a decision-making unit (DMU). Next, those objective functions that needs to be maximized will be used to define the outputs of DMU and those that needs to be minimized will be used to define the inputs of DMU. Consequently, two different fuzzy efficiency scores will be derived for each arc by solving fuzzy DEA models. So, a unique fuzzy attribute will be defined for each arc by combining the resulting fuzzy efficiency scores. Therefore, the FMOTP will be converted into a single objective fuzzy TP that can be solved using the standard algorithms. Finally, using a numerical example the proposed approach has been illustrated.

Efficiencya Assessment and Target Setting Using a Fully Fuzzy DEA Approach

Data envelopment analysis (DEA) is a non-parametric methodology for efficiency assessment. This paper proposes a new radial, input-oriented and fully fuzzy DEA approach, based on an LU-fuzzy partial order (L for lower, U for upper), for assessing the relative efficiency of a set of Decision-Making Units (DMUs). The proposed approach involves a radial input contraction, Phase I, and an additive slacks maximization, Phase II. Each phase is first formulated as a fully fuzzy linear programming (FFLP), and then it is transformed into a multiobjective optimization problem. The latter is solved using the lexicographic weighted Tchebycheff method. The proposed fully fuzzy DEA approach provides, for each unit, a fuzzy efficiency measure and a fuzzy target operating point. A classification of the efficiency status of the units is also presented. Computational experiences and comparison with other fuzzy DEA approaches are reported.

Assessment of Energy Systems Using Extended Fuzzy AHP, Fuzzy VIKOR, and TOPSIS Approaches to Manage Non-Cooperative Opinions

Energy systems planning commonly involves the study of supply and demand of power, forecasting the trends of parameters established on economics and technical criteria of models. Numerous measures are needed for the fulfillment of energy system assessment and the investment plans. The higher energy prices which call for diversification of energy systems and managing the resolution of conflicts are the results of high energy demand for growing economies. Due to some challenging problems of fossil fuels, energy production and distribution from alternative sources are getting more attention. This study aimed to reveal the most proper energy systems in Saudi Arabia for investment. Hence, integrated fuzzy AHP (Analytic Hierarchy Process), fuzzy VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje) and TOPSIS (Technique for Order Preferences by Similarity to Idle Solution) methodologies were employed to determine the most eligible energy systems for investment. Eight alternative energy systems were assessed against nine criteria—power generation capacity, efficiency, storability, safety, air pollution, being depletable, net present value, enhanced local economic development, and government support. Data were collected using the Delphi method, a team of three decision-makers (DMs) was established in a heterogeneous manner with the addition of nine domain experts to carry out the analysis. The fuzzy AHP approach was used for clarifying the weight of criteria and fuzzy VIKOR and TOPSIS were utilized for ordering the alternative energy systems according to their investment priority. On the other hand, sensitivity analysis was carried out to determine the priority of investment for energy systems and comparison of them using the weight of group utility and fuzzy DEA (Data Envelopment Analysis) approaches. The results and findings suggested that solar photovoltaic (PV) is the paramount renewable energy system for investment, according to both fuzzy VIKOR and fuzzy TOPSIS approaches. In this context our findings were compared with other works comprehensively.

A Credibilistic Fuzzy DEA Approach for Portfolio Efficiency Evaluation and Rebalancing Toward Benchmark Portfolios Using Positive and Negative Returns

This paper proposes a data envelopment analysis (DEA)-based portfolio efficiency evaluation approach integrated with a rebalancing method to help investors acquire efficient portfolios. Two fuzzy portfolio selection models with value at risk (VaR) and conditional value at risk (CVaR) as objectives are proposed under the credibilistic framework. The models are constrained by realistic constraints of short selling/no short selling, capital budget, bounds on investment in an asset, and minimum return desired by the investor. These models are used to compute the benchmark portfolios, which constitute the portfolio efficient frontier. Furthermore, random sample portfolios are generated individually for each model in compliance with their constraints. These random sample portfolios are evaluated in terms of their relative efficiency with risk (VaR or CVaR) as an input and return as an output using DEA. Bearing in mind the volatile nature of the investment market, negative returns are also considered for portfolio efficiency evaluation using the range directional model. Moreover, an efficiency frontier improvement algorithm is used to rebalance the inefficient random portfolios to make them efficient. The proposed approach provides an alternative to the investors to acquire benchmark portfolios using the traditional portfolio selection models. A detailed numerical illustration and an out of sample analysis with the Nifty 50 index from the National Stock Exchange, India, are presented to substantiate the proposed approach.

Fuzzy ANP and DEA approaches for analyzing the human development and competitiveness relation

Human development and competitiveness have a causal relation. However, the literature is not clear on which one affects the other. This study investigates the bilateral relation between human development and competitiveness. For this purpose, initially, Fuzzy Analytic Network Process (FANP) is utilized to develop a composite index based on the relative importance weights of respective human development and competitiveness drivers. By FANP, the effects of key dimensions of human development and indexes of competitiveness on each other are taken into account. Subsequently, countries’ efficiencies on converting their human development to competitiveness and inversely, competitiveness to human development is measured by Data Envelopment Analysis (DEA). Two different DEA models are developed to consider the bilateral relations. 45 countries are evaluated using both FANP and DEA models. Finally, the results are synthesized to reveal the direction of the relationship. It is found that the effect of competitiveness on human development is more significant than the effect of human development on competitiveness.

The measurement of agricultural productivity change in OECD countries with Fuzzy data

In this paper, we aim to measure agricultural productivity change of 34 OECD countries between years 1990 and 2014. The methods employed are data envelopment analysis (DEA) and malmquist productivity index (MPI). DEA is a relative efficiency method in a production technology, whereas MPI is based on DEA to measure the changes in the production technology over time. Our challenge is the existence of missing data points over the years in the initial dataset, which correspond to approximately 9% of the data. Removing units, factors or years with missing data as commonly practiced in DEA, would cause loss of information and makes it very difficult to draw conclusions in such a macro-data. We present the idea of using averages of available data points for a given factor and average variations over the years in those data to produce intervals for the missing points and handle the problem without any dimension reduction in the available data. Fuzzy DEA approach is employed using the calculated factor-specific intervals followed by MPI calculations to conduct a productivity change analysis. We suggest and empirically illustrate that instead of narrowing down the scope of the analysis by excluding the points missing, applying fuzzy approaches is an option worth considering by which it can be possible to make the best out of the available information. The results of the analysis are interpreted with respect to years, countries, regions and economic size of the countries.

On the importance of perspective and flexibility for efficiency measurement: effects on the ranking of decision-making units

The efficiency of a firm can be assessed from several perspectives and using a variety of methodologies. Data envelopment analysis (DEA) is one of the most commonly used methodologies. Conventional DEA analyses or models allow one to classify decision-making units (DMUs) into efficient and inefficient ones based on their efficiency scores, which could also be used for ranking DMUs; however, such rankings generally show many ties. Super-efficiency DEA analyses have been proposed to address the tie issue. On the other hand, conventional DEA analyses only take account of a single perspective in estimating efficiency scores. Cross-efficiency DEA analyses provide an alternative that takes account of the perspectives or perceptions of different DMUs. Conventional DEA analyses designed for handling crisp data have also been extended to deal with fuzzy data. In this paper, we propose a fuzzy version of cross-efficiency DEA analysis along with a method for ranking DMUs. We illustrate our proposal with a real example from the Spanish banking sector. In order to assess the robustness of our proposal, we compared our results with those obtained with three different approaches based on the perspective from which efficiency aims to be evaluated: a fuzzy DEA approach, a cross-efficiency-based approach and a TOPSIS-based approach.