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4 Conclusions
After completing the **data** **envelopment** **analysis** model applying for 25 property and casualty insurance companies, the team was able to research and thus have a deeper understanding of the DEA model, applying linear programming method to some two-input-one- output DEA problems with both mathematical approach and excel solver approach, testing the change of the efficient frontier line caused by further constraints of input/out weights from both numerical prospective and graphical prospective, and eventually applying DEA model with pre- set weight constraints to evaluate 25 property and casualty insurance companies with five inputs and four outputs. Since the **data** was not provided, the team has also spent a fair amount of time to determine the input and output factors, a list of companies, the source **data**, as well as to clean up and adjust some **data** to fit the DEA model.

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Because of the Asian financial crisis and financial regulations, the Korean banking industry adopted the new internet bank system later than other major economies, so did the implementation of regulations and permits for internet-only banks. Because of this, the importance and accountability of public policymakers have increased. Thus, The Korean government started regulatory sandbox in 2019(2019, The Korea Herald). As a part of the new financial institution, there is an increasing interest in internet-only banks, which started operating in 2017. To understand online banking industry, this paper has examined the empirical technical efficiency of 14 number of Korea banks from 2017 to 2019. To compare the relative efficiency rate of commercial, local, and internet banks in Korea, we used a **data** **envelopment** **analysis** method to find the technical and scale efficiency of internet-only banks(K-bank, Kakao bank).

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e-mails: jk_ct@hotmail.com, wongky@fkm.utm.my, farzad_behrouzi@yahoo.com
Abstract—This paper is a review paper focusing on the methodological development of **Data** **Envelopment** **Analysis** (DEA), a multi-factor performance measurement and improvement tool. Since its introduction in 1978, vast studies have been done on DEA, causing significant growth in its methodology and applications in the real world. The purpose of this paper is to provide a general introduction to DEA. The basic DEA models and some important methodological extensions of DEA, such as multilevel DEA models, stochastic DEA models, and fuzzy DEA models, are discussed in the paper. In addition, some current and future research trends are highlighted.

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A preprint of the article to be published in European Journal of Operational Research *
Abstract
Measuring economic efficiency requires complete price information, while resorting to technical efficiency exclusively does not allow one to utilise any price information. In most studies, at least some information on the prices is available from theory or practical knowledge of the industry under evaluation. In this paper we extend the theory of efficiency measurement to accommodate incomplete price information by deriving upper and lower bounds for Farrell's overall economic efficiency. The bounds typically give a better approximation for economic efficiency than technical efficiency measures that use no price **data** whatsoever. From an operational point of view, we derive new **Data** **Envelopment** **Analysis** (DEA) models for computing these bounds using standard linear programming. The practical application of these estimators is illustrated with an empirical application to large European Union commercial banks.

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The **Data** **Envelopment** **Analysis** Toolbox covers a wide variety of models calculating effi- ciency and productivity measures in an organized environment for MATLAB. The models implemented correspond to the classic radially oriented, the directional model and the addi- tive formulation. Both constant and variable returns to scale technical efficiency measures are calculated, which allows the calculation of scale efficiency. The economic performance of firms in terms of technical and allocative criteria is also presented, along with efficiency models including undesirable outputs. Models that overcome the low discriminatory power of the standard DEA models such as the super-efficiency or cross efficiency model are also included. Productivity indices are also implemented, both the standard Malmquist index based on radial efficiency, and the Malmquist-Luenberger defined in terms of the directional distance function. Finally, statistical analyses and hypotheses testing using bootstrapping techniques are also available.

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Keyword: **Data** **envelopment** **analysis**, Integer **data**, Capacity Utilization.
1. Introduction
Capacity Utilization deals with a situation where some of the input values are fixed and cannot simply be changed, while others are flexibly changed. Therefore, we classify inputs into fixed and variable inputs and accordingly evaluate the effect of productivity of variable inputs. The consolidation of variable inputs, whether increases or not the efficiency value of evaluation decision making unit (DMU). Researcher such as Fare et al. [7] and Coilli et al. [3] have developed capacity utilization within the framework of **data** **envelopment** **analysis** (DEA). Tone [4] expanded SBM model for evaluation capacity utilization.

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Keywords: DEA, Context-Dependent, Interval **Data**, Interval Attractiveness, Interval Progress
1. Introduction
**Data** **envelopment** **analysis** (DEA), developed by Char- nes et al. [1], usually evaluates decision making units (DMUs) from the angle of the best possible relative effi- ciency. If a DMU is evaluated to have the best possible relative efficiency of unity, then it is said to be DEA ef- ficient; otherwise it is said to be DEA inefficient. Per- formance of inefficient DMUs depends on the efficient DMUs, that is, the inefficiency scores change only if the efficiency frontier is altered.

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Received June 8, 2016, Accepted September 19, 2106 Abstract
**Data** **Envelopment** **Analysis** (DEA) is a mathematical programming for evaluating efficiency of a set of Decision Making Units (DMUs). One of the problems in DEA, is distinguishing outlier DMUs which have a different behavior in contrast to the general prevailing behavior of the population. The important issue is that the outlier DMUs, which are caused by the incorrect way of collecting **data** or other unknown factors which can be social, political and etc. , can affect the efficiency of other DMUs. Thus, recognizing and excluding them from the population or reducing their effect and proportioning their status with the population can influence the improvement of total efficiency of population.

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3 Results and discussions
In this section, the proposed MOLP interactive procedure is applied to search for MPSs along the efficient frontier to the United Kingdom (UK) retail bank industry. The **data** set collected from Wong and Yang (2004) through a study on **data** **envelopment** **analysis** and multiple criteria decision making based on the evidential reasoning approach-performance measurement of UK retail banks (Yang (2001);Yang and Xu (2002)). It is mentionable that the **data** has been changed from exact to interval to be more suitable for the research in this paper.

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Keywords: **data** **envelopment** **analysis**; eﬃciency **analysis**; marble factories
Introduction
One of the main reasons that developed countries are economically strong is the ability of these countries to beneﬁt from their natural resources in the best way possible. The fact that the amount and values of the European Community member countries are high in terms of world marble trade reﬂects this situation very well. These countries import mar- ble blocks from other countries and process incompletely processed marble slabs which are exported into the third world countries for added proﬁts. % of the marble export in the world is carried out by six countries which are Italy, China, India, Spain, Brazil and South America has an important share. Out of these countries, while India, China, Brazil

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- The possibilities of **data** **envelopment** **analysis** models go beyond measuring the efficiency of hospitals but can be used to measure quality, planning, and others through the use of appropriate variables and models. Differences in performance between these hospitals.
In recent years, limitation of resources in health services, which is an important issue for individuals and community life, the continuous increase in health expenditures, changes in disease structure, innovations in medical science and technology and also competition among service providers require health services to be delivered effectively and efficiently. For this reason, businesses continuously measure their efficiency. **Data** **envelopment** **analysis** (DEA) is one of the widely used efficiency measuring method in the literature, (Yazdian et al., 2016). But, there is no common DEA model to meet the needs of all businesses, (Raei, Yousefi, Rahmani, Afshari, & Ameri, 2017). Each Business chooses the appropriate input and output variables according to their structure. The selection of input or output variables is an important issue that varies depending on what you want to see as an output, which inputs or environmental factors are more likely to affect this output. Therefore, the input and output variables used to compare the relative efficiencies of decision-making units are selected with great care and accuracy, (C.

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The motivation of this study is to propose an equitable method for ranking decision making units (DMUs) based on the **data** **envelopment** **analysis** (DEA) concept. For this purpose, first, the minimum and maximum efficiency values of each DMU are computed under the assumption that the sum of efficiency values of all DMUs is equal to unity. Then, the rank of each DMU is determined in proportion to a combination of its minimum and maximum efficiency values.

A “must-do” for the sellers, in particular, is to understand patterns of investment and reward, and effectively manage the process that defines the dynamics of buyer-seller evolution. This paper tries to use **data** **envelopment** **analysis** as a reliable and achievable tool for performance evaluating, quality and performance improvement of Buyer-Seller Relationship, in the situation where the information flows are imprecise **data** between buyers and sellers.

In this paper we tried to achieve two main goals. First, we converted and developed the Period **Data** **Envelopment** **Analysis** to a fuzzy modelas we made the RBS numbers consideringthe mean, standard deviation, maximum and minimum of data.Then we converted the fuzzy model to a simple model using the preference method. The importance and advantage of this method is in this point that as we know, most of fuzzy solutions are based ondifferent s and making the results with different , brings some difficulties in final results and efficiency calculations, but using our method, applying just one simple model in that we use equivalence multiplier instead of main **data**, we can attain the relation efficiencies which is the final conclusion in easiest manner.

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Measuring the efficiency of banking industry has attracted considerable attention by academics, policymakers, and other market participants all over the world (e.g. Yue, 1992; Tahir et al., 2009). However, these studies ignored several areas related to banking efficiency **analysis**. First of all, very few studies (e.g. Al Tamimi and Lootah, 2007; Avkiran, 2009) have only addressed the operational and profitability efficiency of the UAE banks and ignored the other indicators of the efficiency such as marketability and social disclosure efficiencies. Seiford and Zhu (1999) and Luo (2003) show that marketability efficiency is a vital indicator as well as the profitability efficiency since the real value of a bank should be defined by the current stock market. Second, greater disclosure enhances stock market liquidity thereby reducing cost of equity capital through reducing information asymmetry between management and fund providers (Botosan, 1997; Christensen et al., 2008; Francis et al., 2008; Gao, 2008). In this context, the second stream of environmental disclosure research suggests that a significantly negative association between disclosure and cost of equity capital may be extended to corporate voluntary social reporting. Disclosing information to show socially responsible behaviors can help companies avoid government regulation, gain legitimacy, and reduce compliance costs (Dhaliwal et al., 2009). Furthermore, consumers and investors who care about social and environmental issues prefer socially responsible corporations thereby improving their sales level and financial performance (Lev et al., 2010; Richardson and Welker, 2001). Accordingly, this study contributes to this literature by extending the efficiency **analysis** of the UAE banks based on the following three dimensions: profitability, marketability, and social disclosure efficiencies. The remainder of this paper proceeds as follows: the following briefly reviews the literature on **data** **envelopment** **analysis** (DEA) used in banking efficiency **analysis**. Third section describes procedures used to estimate the level of the UAE banks’ social disclosure. Fourth section presents the DEA that is applied in this study. Fifth section discuses the **data** and empirical results; and the final section summarizes the study’s conclusions, implications, and suggestions for future research.

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the proposed approach was demonstrated by studying a maritime collision risk due to technical failures. Sharma et al. [17] used a fuzzy rule-based inference method and the grey theory for prioritizing failure modes. Fuzzy linguistic terms are used to represent the risk degree for O, S, D and RPNs in the fuzzy rule base. Chin et al. [14] proposed an FMEA using the group-based evidential reasoning (ER) approach to capture FMEA team members’ diversity opinions and prioritize failure modes under diﬀerent types of uncertainties such as incomplete assessment, ignorance and intervals. The risk priority model was developed using the group-based ER approach, which includes assessing risk factors using belief structures, synthesizing individual belief structures into group belief structures, aggregating the group belief structures into overall belief structures, converting the overall belief structures into expected risk scores, and ranking the expected risk scores using the minimax regret approach (MRA). Wang et al. [21] proposed a deﬁnition for the fuzzy RPNs using fuzzy weighted geometric means (FWGM). The fuzzy RPNs can be calculated by using α-level sets and a linear programming model and defuzziﬁed by the centroid defuzziﬁcation method for the ﬁnal ranking of the failure modes. In the method, diﬀerent combinations of O, S and D can produce diﬀerent fuzzy RPNs only when assigning diﬀerent importance weights to O, S and D. In spite of the fact that much eﬀort has been paid to the improvement of RPN, the improved methods either need to specify or determine the weights of risk factors in advance or take no account of them at all. It is argued that the speciﬁcation or determination of risk factor weights is not easy because diﬀerent decision makers (DMs) may have distinct judgments or preferences. Diﬀerent failure modes have diﬀerent consequences. The speciﬁcation or determination of a ﬁxed set of risk factor weights for all the failure modes might be inappropriate, particularly in the case with a large number of failure modes. In other words, it might be a better choice to use diﬀerent sets of risk factor weights for diﬀerent failure modes when there are a large number of failure modes to be prioritized. In this aspect, Garcia et al. [11] proposed a fuzzy **data** **envelopment** **analysis** (DEA) approach for FMEA, which does not require specifying or determining risk factor weights subjectively. Their approach, however, was computationally very complicated and also could not produce a full ranking for the failure modes to be prioritized. In this study we present an integrated model based on a new DEA model and Chin’s approach [6] to prioritize the risk factors. It is shown that the proposed model has better discriminating power than the traditional DEA eﬃciency and Chin’s model [6].

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Received 12 April 2019, Accepted 24 October 2019 Abstract
This study intends to expand a set of proper performance evaluation indices which embraces strategies for sustaining top performance using SWOT **analysis** inside a balanced scorecard (BSC) outline for the large commercial bank branches in IRAN by operating a fuzzy **Data** **Envelopment** **Analysis** (FDEA). Through literature reviews and the banks’ experts and managers opinions and who have real practical experiences in the bank strategy planning, satisfactory performance evaluation indices have been selected throughout SWOT **analysis**.

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Received August, 13, 2016, Accepted April, 23, 2017.
Abstract
Congestion indicates an economic state where inputs are overly invested. Evidence of congestion occurs whenever reducing some inputs can increase outputs. In this paper, we present a new model to identify and evaluate congestion in **Data** **Envelopment** **Analysis** (DEA). We use output efficient DMUs to construct our proposed model to evaluate congestion. We also proposed a linear inequality and equality system to identify the occurrence of congestion. Finally, three numerical examples are presented to illustrate the use of our proposed method.

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