International Journal of Data Envelopment Analysis
Volume:10 Issue: 4, Nov 2022

Meta Cost Malmquist Index explains change of cost productivity of Decision Making Unit (DMUs) in several time periods. The Trade Offs approach is an advanced tool for the improvement of the discrimination of Data Envelopment Analysis (DEA) models. They used CRS models in DEA for computing this index, since the convexity assumption is strong condition for computing, so for solving this problem in this paper we use Free Disposal Hull (FDH) models in DEA for computing Meta Cost Malmquist Index. Also in this paper Meta Cost Malmquist Index is evaluated considering in fact that relative importance of input and outputs id different periods are different. In the papers concerning Meta Cost Malmquist Index this fact is not considered, which is very important from managerial point of you. The main advantage this index is that, it is circular.

When we use the CCR model in the input-oriented with fuzzy data for ranking with the help of cross-efficiency, there is a possibility that the model will find a different optimal answer. This means that the ranking is not unique, that is, a decision-making unit may be assigned several ranks. Here, the judgment regarding the ranking faces a problem. To solve this problem, a secondary objective is determined for weight selection. According to that secondary objective, a suitable weight is selected from among the optimal solutions. In this article, the secondary goal of the concept of symmetrizing the weights plays a fundamental role in solving the mentioned problem. The model selects weights that are symmetrical, the act of choosing symmetrical weights causes many weights that are not useful to be removed from the set. The decision-making unit that selects symmetrical weights for all indicators, has a better performance than the decision-making unit that does not use symmetrical weights and covers its weak points with low weight and highlights its strong points with high weight. The model along with the mentioned secondary objective is used to evaluate decision-making units with fuzzy input and output, by choosing the optimal weight, a cross-efficiency table is formed. By using the cross-efficiency table, the efficiency of each unit is determined and ranked compared to other units. Units are done.

This study combines Data Envelopment Analysis (DEA) with machine learning clustering method in datamining for finding the most efficient Decision Making Unit (DMU) and the best clustering algorithm, respectively. The problem of assessment of units by using DEA may not be straightforward due to the data uncertainty. Several scholars have been attracted to develop methods which incorporate uncertainty into input/output values in the DEA literature. On the other hand, in many real world applications, the data is reported in the form of intervals. This means that each input/output value is selected from a symmetric box. In the DEA literature, this type of uncertainty has been addressed as Interval DEA approaches. The main goal of this study is to evaluate the efficiency of banks in the case of data uncertainty with cross-efficiency method in the DEA literature. For this purpose, we consider the BCC-CCR and CCR-BCC models in the presence of uncertain data to find the superior model. After applying the optimization models, in machine learning step, clustering method is applied. Clustering is a procedure for grouping similar items together which this group is called the cluster. Also, the different clustering algorithms can be used according to the behavior of data. In this study, we apply the farthest first and expectation maximization algorithms and show that, in the case of data uncertainty, the BCC-CCR and farthest first algorithms are as a superior optimization model and machine learning algorithm, respectively.

Data Envelopment Analysis (DEA) is an extremely flexible and useful methodology, which provides a relative efficiency score for each decision-making unit.Classic DEA models only evaluate the performance efficiency of units and they cannot provide any information about the progress and regress of units in two periods. Also, they suppose that all inputs and outputs are positive real numbers. But in the real world, due to the existence of uncertainty, this assumption may not always be true. So, the DEA models with fuzzy data (FDEA models) can more realistically represent real-world problems than the conventional DEA models. In this paper, we assume all inputs, outputs and efficiency measures are triangular fuzzy numbers. So we present a method for obtaining the fuzzy Malmquist productivity index on fuzzy data, and finally, we can determine progress and regression for units with fuzzy data.

In this paper, we propose a new hybrid neural network including Data Envelopment Analysis(DEA) and Radial Basis Function Network (RBFN)for binary classification problems. In the supervised learning phase of the neural network, the additive model is used to learn the classification function and Gaussian Radial Basis Function (GRBF) is used in the unsupervised learning phase of the neural network. Compared with the existing RBFN-DEA model for solving classification problems, the proposed model has low CPU time and can be applied to solve classification problems with negative data.