Fuzzy Data Envelopment Analysis Research Articles

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.

Solving Generalized DEA/AR Model With Fuzzy Data and Its Application to Evaluate the Performance of Manufacturing Enterprises

The use of conventional data envelopment analysis (DEA) models in real-world problems are limited because of some restrictions that must be considered in the model such as imprecise or vague data in inputs and outputs as well as additional information or assumptions. One way to handle this problem is by using fuzzy DEA with assurance regions (FDEA/AR) models. There is a common approach in almost all the suggested methods for solving FDEA/AR models. However, in this paper, we show that in some DEA/AR models, applying this approach can be led to inappropriate results. Four theorems are given to provide some sufficient conditions for a DMU to be the DEA/AR efficient. These theorems can be used to check the accuracy of the presented methods for solving FDEA/AR models, too. Moreover, a new method for solving a generalized FDEA/AR model that includes established DEA models such as CCR model (Charnes et al., 1978), BCC model (Banker et al., 1984), FG model (Fare & Grosskopf, 1985), and ST model (Seiford & Thrall, 1990) is proposed. These models are constant, variable, non-decreasing, and non-increasing returns to scale models, respectively. The proposed method is applied to evaluate the performance of manufacturing enterprises.

Resilience-Based Efficiency Measurement of Process Industries with Type-2 Fuzzy Sets

Today’s business environments are prone to high levels of uncertainties and risks because the speed of changes is too high. Hence, the way of dealing with threats has changed. Complex socio-technical systems (CSSs) are confronted with out-of-control disturbances that need risk management systems to be applied. Risk management is organized activities to monitor and control risks in CSSs. Newly, resilience engineering (RE) as a safety management discipline has been expanded to change the attitude to risks. RE is defined as the capability of a system to absorb disturbances and adapt to rapidly changing conditions. Process industries as CSS, are potentially disposed to catastrophic events such as explosions, toxic leakages, stoppages of production operations, etc. In this paper, a novel RE-based algorithm is developed to measure the efficiency of process industries for preventing and reducing disorders considering their high-level of uncertainty. To do this, firstly, resilience indices in an oil refinery as an essential process industry are extracted. Then, using type-2 fuzzy data envelopment analysis (DEA), a new multi-objective approach is presented to evaluate the efficiency of DMUs from the perspective of RE. Interval type-2 fuzzy sets (IT2 FSs) is used in this approach because they potentially hold more implication than the classical type-1 fuzzy sets (T1 FSs). As a case study, a refinery as a CSS is evaluated. Using the proposed algorithm shows the efficiency scores of DMUs in the refinery. By conducting a comparative analysis, it was revealed that the proposed model outperforms classical methods. The results of the proposed approach show that besides simplicity, there is good stability to consider the criteria of RE in efficiency measurement with IT2 FSs.

A New Fuzzy DEA Model for Solving the MCDM Problems in Supplier Selection

Supplier selection is a crucial task in supply chain management, and good supply chain management is essential to a company's ability to develop sustainably and gain the trust and satisfaction of its customers. In modern supply chain management, supplier selection often takes the form of a multi-criteria decision-making (MCDM) problem. Thus, to solve this problem, this study formulated a novel fuzzy MCDM model, which is based on the fuzzy data envelopment analysis model. This novel approach can transform the linguistic variables of assessment criteria into well-founded quantitative data for calculation. Moreover, our approach can effectively discriminate between decision-making units (both efficient and inefficient) to aid managers in identifying the most suitable suppliers. We hope that our model can provide scholars and managers with new insights into solving the MCDM problem in supplier selection.

Portfolio Selection Using Data Envelopment Analysis Cross-Efficiency Evaluation with Undesirable Fuzzy Inputs and Outputs

In this paper, we discuss a portfolio selection problem based on fuzzy data envelopment analysis cross-efficiency evaluation wherein both undesirable fuzzy inputs and outputs have been considered. We first propose a data envelopment analysis cross-efficiency model, in which both undesirable inputs and outputs are considered. Furthermore, considering the imprecision of the data, we extend the crisp model to the fuzzy environment and propose a fuzzy data envelopment analysis cross-efficiency model with coexisting undesirable input and output data. We then apply the proposed model to the portfolio selection problem and present a novel mean-semivariance portfolio selection model based on fuzzy data envelopment analysis cross-efficiency scores, in which several realistic constraints are considered, including a budget, cardinality, buy-in thresholds, and no short selling constraints. After that, we employ the genetic algorithm (GA) to solve the proposed model. Finally, a real-life case study is presented to demonstrate the effectiveness of the proposed approaches.

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.

Forecasting the Confidence Interval of Efficiency in Fuzzy DEA

Data Envelopment Analysis (DEA) is a well-known method that based on inputs and outputs calculates the efficiency of decision-making units (DMUs). Comparing the efficiency and ranking of DMUs in different time periods lets the decision makers to prevent any loss in the productivity of units and improve the production planning. Despite the merits of DEA models, they are not able to forecast the efficiency of future time periods with known input/output records of the DMUs. With this end in view, this study aims at proposing a forecasting algorithm with a 95% confidence interval to generate fuzzy data sets for future time periods. Moreover, managers’ opinions are inserted in the proposed forecasting model. Equipped with the forecasted data sets and with respect to the data sets from previous periods, this model can rightly forecast the efficiency of the future time periods. The proposed procedure also employs the simple geometric mean to discriminate between efficient units. Examples from a real case including 20 automobile firms show the applicability of the proposed algorithm.

Dynamic setting of shipping points in logistics systems with multiple heterogeneous warehousesorecasting the confidence interval of efficiency in fuzzy DEA

This study aims to model a planning process of handling outbound deliveries from a set of geographically dispersed warehouses. The model incorporates parameters observed in real life supply chains and allows simulation of various variants of process supporting decision making of current shipment management, as well as strategic planning of distribution network. A heuristic algorithm that can be used for planning of source warehouses for shipments is proposed. The model is built and tested on real business data and its performance proves to be better than the one currently used by reference company.

A novel decision-making method using fuzzy DEA credibility constrained and RC index

Decision-making based on expert’s opinion by data envelopment analysis (DEA) models requires crisp number. However, the assumption of expert might not always be accurate. This paper introduces fuzz...

A fuzzy DEA approach on the extended transportation problem

A fuzzy DEA approach on the extended transportation problem

Determining the Relative Efficiency of Container Terminals in Turkey Using Fuzzy Data Envelopment Analysis

In this study, fuzzy data envelopment analysis (FDEA) was conducted to determine the relative efficiency of the container terminals operating in Turkey. For this purpose, the data from the container terminals were converted into fuzzy values using the “set of α cuts approach” and the upper and lower limit values for each terminal were determined. The lower and upper limit efficiency values were calculated using the input-oriented CCR-FDEA method. The minimax regret approach was used to sort and compare the relative efficiency of terminals. According to the resulting efficiency scores, one container terminal was effective at all α cutting levels. It was calculated that the four container terminals had the lowest values at all α cutting levels regarding the maximum efficiency loss values of other container terminals.

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.

Improving the performance of a medical imaging center through simulation and fuzzy DEA

Given that various operational methods can be considered for a system, applying changes to study the results and determine the best operational technique is costly and disrupts the system. Thus, to analyze and evaluate the outcomes of employing different operational methods, simulation is utilized. In this study, to improve the performance of a medical imaging center (MIC), first, this center was simulated and then, different scenarios were defined and simulated. Subsequently, using the simulation results and for evaluating the scenarios through Data Envelopment Analysis (DEA), each scenario was considered as a decision making unit (DMU). Since simulation results of each scenario are uncertain and differ for different iterations, a method was utilized capable of using the results of all iterations. On the other hand, indexes such as satisfaction, patient’s appropriate waiting, helpful servicing with the least number nurses and the maximum number services that have fuzzy nature, are important factors for MIC. Therefore, using the simulation results and considering the system manager’s idea, a method was proposed for determining the fuzzy values of these indexes. Next, a ranking model and an algorithm were proposed for determining a unique ranking and introducing the best scenario to improve the performance of MIC.

Modified Fuzzy Data Envelopment Analysis Models

This paper examines the use of data envelopment analysis (DEA) in the conduct of efficiency measurement involving fuzzy (interval) input-output values. Data envelopment analysis is a linear programming method for comparing the relative productivity (or efficiency) of multiple service units. Standard DEA models assume crisp data for both the input and output values. In practice however, input and output values may be uncertain, vague, imprecise or incomplete. A new pair of fuzzy DEA models is presented which differs from existing fuzzy DEA models handling uncertain data. In this approach, upper bound interval data are used exclusively to obtain the upper frontier values while lower bound interval data are used exclusively to obtain the lower frontier values. The outcome, when compared with the outcome of existing approach, based on the same set of data, shows a swap in the upper and lower frontier values with exactly the same number of efficient decision making units (DMUs). This new approach therefore clears the ambiguity occasioned by the mixture of upper and lower bound values in the determination of the upper and lower frontier efficiency scores respectively.

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

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.

Development of two-stage parallel-series system with fuzzy data: A fuzzy DEA approach

We consider a two-stage parallel-series system having three sub-systems. The independent two sub-systems of the first stage are linked in parallel and then linked to the third sub-system of the second stage in series. The deterministic two-stage parallel-series system approach is extended to uncertain/imprecise environment where the data are represented as fuzzy numbers. Using the Zadeh extension principle, we develop a fuzzy two-stage parallel-series system to determine the lower and upper bound fuzzy efficiencies of the decision-making units with the help of $$\alpha -$$ cut and rank the DMUs using the ranking index approach. The proposed methodology is illustrated using the case of Taiwan’s non-life insurance companies.

Solving the fully fuzzy multi-objective transportation problem based on the common set of weights in DEA

A transportation problem basically deals with the problem which aims to minimize the total transportation cost or maximize the total transportation profit of distributing a product from a number of sources or origins to a number of destinations. While, in general, most of the real life applications are modeled as a transportation problem (TP) with the multiple, conflicting and incommensurate objective functions. On the other hand, for some reason such as shortage of information, insufficient data or lack of evidence, the data of the mentioned problem are not always exact but can be fuzzy. This type of problem is called fuzzy multi-objective transportation problem (FMOTP). There are a few approaches to solve the FMOTPs. In this paper, a new fuzzy DEA based approach is developed to solve the Fully Fuzzy MOTPs (FFMOTPs) in which, in addition to parameters of the MOTPs, all of the variables are considered fuzzy. This approach considers each arc in a FFMOTP as a decision making unit which produces multiple fuzzy outputs using the multiple fuzzy inputs. Then, by using the concept of the common set of weights (CSW) in DEA, a unique fuzzy relative efficiency is defined for each arc. In the following, the unique fuzzy relative efficiency is considered as the only attribute for the arcs. In this way, a single objective fully fuzzy TP (FFTP) is obtained that can be solved using the existing standard algorithms for solving this kind of TPs. A numerical example is provided to illustrate the developed approach.

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.