Fuzzy Efficiency Measures in Data Envelopment Analysis Using Lexicographic Multiobjective Approach

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.There is an extensive literature in data envelopment analysis (DEA) aimed at evaluating the relative efficiency of a set of decision-making units (DMUs). Conventional DEA models use definite and precise data while real-life problems often consist of some ambiguous and vague information, such as linguistic terms. Fuzzy sets theory can be effectively used to handle data ambiguity and vagueness in DEA problems. This paper proposes a novel fully fuzzified DEA (FFDEA) approach where, in addition to input and output data, all the variables are considered fuzzy, including the resulting efficiency scores. A lexicographic multi-objective linear programming (MOLP) approach is suggested to solve the fuzzy models proposed in this study. The contribution of this paper is fivefold: (1) both fuzzy Constant and Variable Returns to Scale models are considered to measure fuzzy efficiencies; (2) a classification scheme for DMUs, based on their fuzzy efficiencies, is defined with three categories; (3) fuzzy input and output targets are computed for improving the inefficient DMUs; (4) a super-efficiency FFDEA model is also formulated to rank the fuzzy efficient DMUs; and (5) the proposed approach is illustrated, and compared with existing methods, using a dataset from the literature

An efficiency evaluation problem including fuzzy weights

This paper presents a procedure to dissolve a fuzzy weights CCR model with numerical input and output data in the objective function. This technique is a combination of utilizing fuzzy operations arithmetic and traditional method in DEA in order to convert the model into two simple linear programming problems with the purpose of detecting the effect of uncertain factors on the efficiency scores of decision making units (DMUs). It is in accordance with our determination to provide a method based on data envelopment analysis (DEA), supporting efficiency evaluation problems in fold fuzziness in factor weights to assist decision making issues

Fuzzy Efficiency Measure with Fuzzy Production Possibility Set

The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. The notion of fuzziness has been introduced to deal with imprecise data. Fuzzy DEA models are made more powerful for applications. This paper develops the measure of efficiencies in input oriented of DMUs by envelopment form in fuzzy production possibility set (FPPS) with constant return to scale

Fuzzy data envelopment analysis:a discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on a-cut. One drawback of the a-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the a-cut approach. We introduce the concept of "local a-level" to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method

Measuring Technical Efficiency of Dairy Farms with Imprecise Data: A Fuzzy Data Envelopment Analysis Approach

This article integrates fuzzy set theory in Data Envelopment Analysis (DEA) framework to compute technical efficiency scores when input and output data are imprecise. The underlying assumption in convectional DEA is that inputs and outputs data are measured with precision. However, production agriculture takes place in an uncertain environment and, in some situations, input and output data may be imprecise. We present an approach of measuring efficiency when data is known to lie within specified intervals and empirically illustrate this approach using a group of 34 dairy producers in Pennsylvania. Compared to the convectional DEA scores that are point estimates, the computed fuzzy efficiency scores allow the decision maker to trace the performance of a decision-making unit at different possibility levels.fuzzy set theory, Data Envelopment Analysis, membership function, α-cut level, technical efficiency, Farm Management, Production Economics, Productivity Analysis, Research Methods/ Statistical Methods, Risk and Uncertainty, D24, Q12, C02, C44, C61,

Supplier selection with support vector regression and twin support vector regression

Tedarikçi seçimi sorunu son zamanlarda literatürde oldukça ilgi görmektedir. Güncel literatür, yapay zeka tekniklerinin geleneksel istatistiksel yöntemlerle karşılaştırıldığında daha iyi bir performans sağladığını göstermektedir. Son zamanlarda, destek vektör makinesi, araştırmacılar tarafından çok daha fazla ilgi görse de, buna dayalı tedarikçi seçimi çalışmalarına pek sık rastlanmamaktadır. Bu çalışmada, tedarikçi kredi endeksini tahmin etmek amacıyla, destek vektör regresyon (DVR) ve ikiz destek vektör regresyon (İDVR) teknikleri kullanılmıştır. Pratikte, tedarikçi verisini içeren örneklemler sayıca oldukça yetersizdir. DVR ve İDVR daha küçük örneklemlerle analiz yapmaya uyarlanabilir. Tedarikçilerin belirlenmesinde DVR ve İDVR yöntemlerinin tahmin kesinlikleri karşılaştırılmıştır. Gerçek örnekler İDVR yönteminin DVR yöntemine kıyasla üstün olduğunu göstermektedir.Suppliers’ selection problem has attracted considerable research interest in recent years. Recent literature show that artificial intelligence techniques achieve better performance than traditional statistical methods. Recently, support vector machine has received much more attention from researchers, while studies on supplier selection based on it are few. In this paper, we applied the support vector regression (SVR) and twin support vector regression (TSVR) techniques to predict the supplier credit index. In practice, the suppliers’ samples are very insufficient. SVR and TSVR are adaptive to deal with small samples. The prediction accuracies for SVR and TSVR methods are compared to choose appropriate suppliers. The actual examples illustrate that TSVR methods are superior to SVR

A stochastic approach for evaluating production planning efficiency under uncertainty

Planning production is an essential component of the decision-making process, which has a direct bearing on the effectiveness of production systems. This study’s objective is to investigate the efficiency performance of decision-making units (DMU) in relation to production planning issues. However, the production system in a manufacturing environment is frequently subject to uncertain situations, such as demand and labor, and this can have an effect not only on production but also on profit. The robust stochastic data envelopment analysis model was proposed in this study with maximizing the number of outputs as the objective function thus means of handling uncertainty in input and output in production planning problems. This model, which is based on stochastic data envelopment analysis and a method of robust optimization, was proposed with the intention of providing an efficient plan of production for each DMU of stage production. The model is applied to small and medium-sized businesses (SMEs), with inputs consisting of the cost of labor, the number of customers, and the quantity of raw materials, and the output consisting of profit and revenue. It has been demonstrated through implementation that the proposed model is both efficient and effective

Evaluating decision-making units under uncertainty using fuzzy multi-objective nonlinear programming

This paper proposes a new method to evaluate Decision Making Units (DMUs) under uncertainty using fuzzy Data Envelopment Analysis (DEA). In the proposed multi-objective nonlinear programming methodology both the objective functions and the constraints are considered fuzzy. The coefficients of the decision variables in the objective functions and in the constraints, as well as the DMUs under assessment are assumed to be fuzzy numbers with triangular membership functions. A comparison between the current fuzzy DEA models and the proposed method is illustrated by a numerical example