Fuzzy Data Envelopment Analysis Model Research Articles

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.

Application of fuzzy DEA and machine learning algorithms in efficiency estimation of paddy producers of rural Eastern India

PurposeData envelopment analysis (DEA) has wide applications in the agricultural sector to evaluate the efficiency with crisp input and output data. However, in agricultural production, impreciseness and uncertainty in data are common. As a result, the data obtained from farmers vary. This impreciseness in crisp data can be represented in fuzzy sets. This paper aims to employ a combination of fuzzy data envelopment analysis (FDEA) approach to yield crisp DEA efficiency values by converting the fuzzy DEA model into a linear programming problem and machine learning algorithms for better evaluation and prediction of the variables affecting the farm efficiency.Design/methodology/approachDEA applications are focused on the use of a common two-step approach to find crucial factors that affect efficiency. It is important to identify impactful variables for minimizing production adversities. In this study, first, FDEA was applied for efficiency estimation and ranking of the paddy growers. Second, the support vector machine (SVM) and random forest (RF) were used for identifying the key leading factors in efficiency prediction.FindingsThe proposed research was conducted with 450 paddy growers. In comparison to the general DEA approach, the FDEA model evaluates fuzzy DEA efficiency giving the user the flexibility to measure the performance at different possibility levels.Originality/valueThe use of machine learning applications introduces advanced strategies and important factors influencing agricultural production, which may help future research in farms' performance.

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.

Measurement Research on Influential Effect of Standardization on Technological Innovation

There is a close relationship between standardization and technological innovation. Based on the analysis of the function mechanism of standardization on technological innovation, this paper has established measurement indexes of the influential effect of standardization on technological innovation. As structural equation modeling (SEM) has its own advantages over statistical methods such as correlation analysis, regression analysis and path analysis, this study attempts to measure the influence degree of standardization on technological innovation by adopting SEM method, and has established a measurement model and a structural equation model for the standardized technological innovation effect. In addition, the study has discussed the fuzzy DEA method to analyze the standardized technological innovation effect of DMUs, established the fuzzy DEA-based index system for evaluating standardized technological innovation effect, constructed the fuzzy DEA model for evaluating standardized technological innovation effect, and provided the solution process of the model.

A new parallel fuzzy data envelopment analysis model for parallel systems with two components based on Stackelberg game theory

This paper investigates the problem of efficiency measurement for parallel systems with two components based on Stackelberg game theory, while some inputs/outputs are fuzzy numbers. Conventional DEA models treat DMUs as “Black Boxes”. While in this paper, we propose a new parallel fuzzy DEA model to calculate the efficiency scores for each DMU’s whole system and its sub-systems. Through the Stackelberg (leader–follower) game theory, the whole system’s efficiency score of each DMU is decomposed into a set of efficiency scores for its sub-systems. This approach is independent of the alpha -cut which reduces the computational efforts. In order to show our method, we use the data from Beasley (J Oper Res Soc 46(4):441–452, 1995) to measure the fuzzy efficiency of the teaching and research efficiencies of chemistry departments in UK universities.

Performance Efficiency of Public Health Sector Using Intuitionistic Fuzzy DEA

Out of several generalizations of fuzzy set theory for various objectives, the notions of intuitionistic fuzzy sets (IFSs) is very useful in modeling real life problems. In existing fuzzy data envelopment analysis (FDEA) models, the inputs and outputs are limited to fuzzy input and fuzzy output data. In real life problems, the input data and output data can be considered as linguistic/vague characterized by intuitionistic fuzzy numbers (IFNs). So, in the present study, we extend FDEA to intuitionistic FDEA (IFDEA) in which the input and output data are taken as IFNs, in particular triangular IFNs (TIFNs). In this study, we develop models to measure the efficiencies of each DMU in intuitionistic fuzzy environment using α and β-cuts and we get IF interval efficiencies. The ranking of FNs has been studied by many authors and extended to IFNs because of its applicability in real life problems. The ranking of IF interval efficiency plays an important role in DEA where the interval analysis is essential. Further, in this paper a new method for ranking IF interval efficiencies has been proposed and compared with other existing methods. A new general minimax approach is proposed to compare and rank the IF efficiency intervals of DMUs. One numerical example is provided to show the applications of the proposed IFDEA model and the proposed ranking approach. Moreover, we present an application of the proposed approach to the public health sector.

Double Frontier Two-Stage Fuzzy Data Envelopment Analysis

Data envelopment analysis (DEA) is a mathematical programming approach with widespread applications in productivity and efficiency analysis. Compared with traditional DEA models, two-stage DEA models show the performance of each process and make available more information for decision making. In an article by Kao and Liu, models were proposed for combining a two-stage process to achieve overall fuzzy efficiency measures. Their method follows the simple geometric average approach and uses the product of two efficiencies. The present article applies a different angle for efficiency analysis in the two-stage fuzzy DEA. We suggest that the overall efficiency score of a decision-making unit (DMU) is defined as total weight of stage efficiencies, not as the simple product of their efficiency. Moreover, the proposed fuzzy DEA models are different from the model by Kao and Liu for fuzzy data in that our models are linear without the need for additional changes in variables and use the same set of constraints to measure the efficiency of DMUs with fuzzy input and output data. While the models by Kao and Liu are a nonlinear optimization problem that need additional changes in variables, and use different sets of constraints to measure fuzzy efficiencies. Additionally, our proposed approach evaluates the performance of DMUs from both optimistic and pessimistic viewpoints. Finally, using the proposed approach, the Taiwanese non-life insurance company problem will be investigated.

Z-ERM DEA integrated approach for evaluation of banks & financial institutes in stock exchange

The purpose of this study is to evaluate efficiency and effectiveness of banks, financial and credit institutes active in stock and super-stock exchange organizations using new Fuzzy DEA model which is the modified, improved and enhanced version of Russell's measurement model. In order to make it more efficient, we used the Z-numbers theory through which the calculations of uncertainty in the decision-making process can be showed more accurately. To do so, the literature of this industry and financial data of the research companies during 2012–2017 were initially overviewed and 16 indicators (indices/indexes) and the main criteria related to their performance evaluation were selected. Afterward, the productivity of banks and financial and credit institutions in different levels of α − cut were specified and compared using integrated approach of ERM and calculations of Z-numbers as well as considering opinions provided by the financial experts with possibility of concurrent evaluation of the efficiency and effectiveness in a model.

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

Many problems in operations research including problems from management, production planning and scheduling, transportation, location, and many others necessitate decision making in the presence of uncertainty. Therefore, many theories and methodologies have been developed to deal with optimization problems under uncertainty in general. To understand uncertain data envelopment analysis models, the process was started by introducing the definition of uncertain variables, uncertain vectors, fuzzy linear programming (FLP). Selection criteria of an incoming vector in improving uncertain linear programming is established along with its unbounded nature. This paper based on the established theoretical framework proposes an alternative linear programming model that can include some uncertainty information. Finally, input-oriented CCR model with fuzzy variables is developed and an effective approach for measuring efficiency is demonstrated with a numerical example.

A common-weights approach for efficiency evaluation in fuzzy data envelopment analysis with undesirable outputs: Application in banking industry

Data Envelopment Analysis (DEA) is a non-parametric approach based on linear programming for evaluating the performance of decision making units (DMUs) with multiple inputs and multiple outputs. The lack of the ability to generate the actual weights, not considering the impact of undesirable outputs in the evaluation process and the measuring of efficiencies of DMUs based upon precise observations are three main drawbacks of the conventional DEA models. This paper proposes a novel approach for finding the common set of weights (CSW) to compute efficiencies in DEA model with undesirable outputs when the data are represented by fuzzy numbers. The proposed approach is based on fuzzy arithmetic which formulates the fuzzy additive DEA model as a linear programing problem and gives fuzzy efficiencies of all DMUs based on resulting CSW. We demonstrate the applicability of the proposed model with a simple numerical example. Finally, in the context of performance management, an application of banking industry in Iran is presented for analyzing the influence of fuzzy data and depicting the impact of undesirable outputs over the efficiency results.

Ranking of decision-making units in Pythagorean fuzzy CCR model using data envelopment analysis

Data envelopment analysis is a mathematical linear programming based method where the overall effectiveness of a set of decision-making units is assessed for accomplishing the task. In this communication, we have projected Pythagorean fuzzy entropy DEA model with the inclusion of the Pythagorean fuzzy information which has a more extensive sense of flexibility in contrast with the intuitionistic fuzzy information. Furthermore, an approach to solve a decision-making problem with Pythagorean fuzzy information has been well presented with a defined set of weights. A numerical example based on evaluation of five government universities has also been provided for illustrating the projected methodology.

Interval Type-2 Trapezoidal Fuzzy Decision- Making Method With Consistency-Improving Algorithm and DEA Model

Interval type-2 fuzzy sets (IT2FSs) are useful and valuable tool to describe the decision makers’ qualitative evaluation information. This paper designs a novel interval type-2 trapezoidal fuzzy decision-making (IT2TFDM) method, in which the local consistency adjustment strategy (LCAS) and interval type-2 fuzzy data envelopment analysis (DEA) are presented. First, in order to sufficiently describe the uncertain evaluation information, the definition of IT2TrFPRs is introduced, which is followed by the presentation of order consistency and multiplicative consistency for IT2TrFPRs. Then, an approach is proposed to check whether an IT2TrFPR is multiplicative consistent, and we construct a convergent consistency-improving algorithm, wherein the LCAS is utilized to retain the preference evaluation information of decision makers as much as possible. Furthermore, in order to determine the interval type-2 trapezoidal fuzzy priority weight vector, we investigate an interval type-2 trapezoidal fuzzy DEA model. An IT2TFDM method is proposed to obtain the reliable ranking of the alternatives. Finally, a fog-haze influence factor selection problem is given to show the practicality of the proposed IT2TFDM method, and the comparative analysis is carried out to clarify its validity and merits.

A new approach using fuzzy DEA models to reduce search space and eliminate replications in simulation optimization problems

This article proposes a new combination of methods to increase optimization simulation efficiency and reliability, utilizing orthogonal arrays, fuzzy-data envelopment analysis (FDEA) with linear membership function, and discrete event simulation (DES). Considering a simulation optimization problem, experimental matrices are generated using orthogonal arrays and which simulation runs (scenarios) will be executed are defined, followed by FDEA to analyze and rank the scenarios in terms of their efficiency (considering occurrence of uncertainty). In this way, it is possible to reduce the search space of scenarios to be simulated, and avoid the need for replications in DES, without impairing the quality of the final solution. Six real cases that were solved by the proposed approach are presented. In order to highlight the efficiency of the proposed method, in Cases 5 and 6, all viable solutions of each of these problems were tested, ie, 100% of the search space was analyzed, and it was found that the solution obtained by the new method was statistically equal to the overall optimal solution. Note that for the other real cases solved, the solutions obtained by the proposed method were also statistically equal to those obtained from the original search space, and that analyzing 100% of the viable solutions space would be computationally impossible or impractical. These results confirmed the reliability and applicability of the proposed method, since it enabled a significant reduction in the search space for the simulation application compared to conventional simulation optimization techniques.

Decision-making model with fuzzy preference relations based on consistency local adjustment strategy and DEA

As one of the most useful tools, fuzzy preference relations (FPRs) can cope with the situations in which the experts are more comfortable providing their evaluation information with numerical values. Consistency-improving process and deriving the reliable priority weight vector for alternatives are two significant and challenging issues in decision making with FPRs. This paper investigates a novel decision-making model with FPRs on the basis of consistency local adjustment strategy and data envelopment analysis (DEA). Firstly, a new approach is proposed to generate the multiplicative consistent FPRs. Subsequently, a convergent consistency-improving algorithm for FPRs is developed to transform the unacceptable multiplicative consistent FPRs into the acceptable ones. In the consistency-improving process for FPRs, the local adjustment strategy is presented to employ decision-maker original evaluation information sufficiently. In order to determine the priority weight vector for alternatives, a novel fuzzy DEA model is constructed. Furthermore, a decision-making model with FPRs is designed to derive the reliable decision-making results. Finally, a numerical example of selecting the most important influence factor for fog–haze is provided, and the comparison with existing approaches is made to validate the rationality and effectiveness of the developed model.

Risk analysis of health, safety and environment in chemical industry integrating linguistic FMEA, fuzzy inference system and fuzzy DEA

Organizations are continuously endeavoring to provide a healthy work environment without any incident, by Health, Safety, and Environment (HSE) management. As most of the activities and processes in the organizations have risk-taking nature, identification and evaluation of risks can be useful to decrease their negative effects on the system. Although Failure Mode and Effect Analysis (FMEA) technique is used widely for risk assessment, the traditional Risk Priority Number (RPN) score has shortcomings like do not considering different weights and the inherent uncertainty of risk factors as well as do not regarding all viewpoints of the experts in decision making. The aim of this study is presenting a hybrid approach based on the Linguistic FMEA, Fuzzy Inference System (FIS) and Fuzzy Data Envelopment Analysis (DEA) model to calculate a novel score for covering some RPN shortcomings and the prioritization of HSE risks. First, after identifying potential risks and assigning values to the RPN determinant factors by linguistic FMEA team members due to the differentiation of these values, FIS is used to reach a consensus opinion about these factors. Then, the outputs of FIS are used by the fuzzy DEA and its supper efficiency model to risk prioritization which can contribute to full prioritization. In addition to considering uncertainty and decreasing dependence on the team’s opinions, in this phase weights of triple factors are calculated based on mathematical programming. To show the ability of the proposed approach in terms of HSE risks prioritization, it has been implemented in an active company in the chemical industry. After identifying risks having high priority based on the proposed score, preventive/corrective actions are presented in accordance with the case study, and for more analysis of results, the self-organizing map has been applied in this study.

Analysing causal relationships between delay factors in construction projects

PurposeAnalyzing factors of delays in construction projects and determining their impact on project performance is necessary to better manage and control projects. Identification of root factors which may lead to project delay and increased cost is vital at the early or planning stage. Better identification of delay factors at the early stage can help the practitioners to reduce their impacts over the long run. Hence, the purpose of this paper is to propose an intelligent method to analyze causal relationships between delay factors in construction projects. The proposed approach is further validated by a real case study of the construction projects in West Azerbaijan province in Iran.Design/methodology/approachDuring the first phase, the fuzzy cognitive map (FCM) is drawn to indicate the causal relationships between the delay factors and the evaluation factors. For this purpose, the causal relationships between 20 delay factors and four evaluation factors are considered. Afterward, the effect of each factor on management goals is evaluated by using a hybrid learning algorithm. Delay factors are further prioritized by applying fuzzy data envelopment analysis (FDEA). In the second phase, an interpretive structural modeling (ISM) is employed to determine the root causes of delay factors.FindingsResults of the first phase show that “supervision technical weaknesses for overcoming technical and executive workshop problems” and “Inaccurate estimation of workload, required equipment and project completion time” are the most significant delay factors. In contrary, “non-use of new engineering contracts” has the lowest impact on the management goals. Meanwhile, the results of the second phase conclude that factors like “Inaccurate estimation of workload, required equipment and project completion time” “weakness of laws and regulations related to job responsibilities” and “lack of foreseen of fines and encouragements in the contracts” are the most significant root factors of delay in construction projects.Originality/valueThis paper integrates three methods including FCM method, FDEA and ISM. In the first phase, FCM is drawn according to the experts’ opinions and concerning management goals and delay factors. Later, these factors are prioritized according to the results of running the algorithm and using the FDEA model. The second phase, the seven-step in the ISM methodology, is done to identify the root factors. To ensure that the root factors of the delay are at a lower level of hierarchical structure, delay factors are partitioned by drawing the ISM model.

A hierarchical fuzzy data envelopment analysis for wind turbine site selection in Indonesia

The Indonesian archipelago has several suitable areas for building wind farms. In the site selection process, apart from wind intensity, there are other factors related to geographical and structural technicality that need to be considered. This research presents a hierarchical fuzzy data envelopment analysis model for identifying suitable locations for the construction of wind farms. The proposed hierarchy consists of two levels that are defined based on the 165 districts and 33 provinces in Indonesia based on data provided by different government organizations. Opinions from experts in different areas were collected and represented by the hesitant fuzzy linguistic term sets, which were converted to optimistic and pessimistic preferences by using linguistic aggregation and, later, integrated to the data envelopment analysis model. Principal component analysis by IBM SPSS was used to verify the importance of the factors that can reduce ineffective indicators from the analysis. The results show that the South Sumatra province has the highest potential for construction of wind farms, especially in the district of Palembang. The West Papua, Papua, and Maluku provinces have descending priority based on good infrastructure accessibility, high wind velocity, and lesser susceptibility to natural disasters.

Dynamic fuzzy data envelopment analysis models: case of bus transport performance assessment

In the transport field, two characteristics–inter-temporal dependency and fuzziness–need to be considered when assessing transport performance. First, input and output levels are inter-temporal dependent due to heavy capital investment and because quasi-fixed input can influence output levels over multiple periods. Second, conventional Data Envelopment Analysis (DEA) models are, in nature, formulated with quantitative variables. However, qualitative measurements that are characterized with “vagueness” or “fuzziness” are as important as quantitative variables for multi-period transport performance assessment. To rectify these problems, the present study extends previous research by proposing a Dynamic Fuzzy Data Envelopment Analysis (DFDEA) method for assessing the comparative efficiency where inter-temporal dependence exists in operating production processes with some “fuzzy” variables. An case study was conducted to evaluate the performance of city bus transport companies in Taipei, Taiwan. Results showed the superiority of the proposed DFDEA model by comparing the results with static models.

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

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.

Fuzzy data envelopment analysis: An adjustable approach

Possibilistic Data Envelopment Analysis (PDEA) is one of the most applicable and popular approaches in the literature to deal with imprecise and ambiguous data in DEA models. In this approach, with respect to tendency of decision maker (DM) in taking optimistic, pessimistic and compromise attitude, three measures including possibility, necessity and credibility measures are used to form the Fuzzy DEA (FDEA) models, respectively. However, decision makers may have different preference and so it is necessary to customize fuzzy DEA models according to properties of DMUs. This paper proposes a novel fuzzy DEA model based on general fuzzy measure in which the attitude of DMUs could be determined by the optimistic-pessimistic parameters. As a result, the proposed FDEA model is general, applicable, flexible, and adjustable based on each DMUs. A numerical example is used to explain the proposed approach while usefulness and applicability of this approach have been illustrated using a real data set to measure efficiency of 38 hospital in United States.