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

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.The first author was partially supported by the research project MTM2017-89577-P (MINECO, Spain). The second author was partially supported by the Spanish Ministry of Economy and Competitiveness, grant AYA2016-75931-C2-1-P and from the Consejería de Educación y Ciencia, Spain (Junta de Andalucía, reference TIC-101). The third author acknowledges the financial support of the Spanish Ministry of Science, Innovation and Universities, grant PGC2018-095786-B-I00

Development of fully intuitionistic fuzzy data envelopment analysis model with missing data: an application to Indian police sector

Data Envelopment Analysis (DEA) is a technique used to measure the efficiency of decision-making units (DMUs). In order to measure the efficiency of DMUs, the essential requirement is input-output data. Data is usually collected by humans, machines, or both. Due to human/machine errors, there are chances of having some missing values or inaccuracy, such as vagueness/uncertainty/hesitation in the collected data. In this situation, it will be difficult to measure the efficiencies of DMUs accurately. To overcome these shortcomings, a method is presented that can deal with missing values and inaccuracy in the data. To measure the performance efficiencies of DMUs, an input minimization BCC (IMBCC) model in a fully intuitionistic fuzzy (IF) environment is proposed. To validate the efficacy of the proposed fully intuitionistic fuzzy input minimization BCC (FIFIMBCC) model and the technique to deal with missing values in the data, a real-life application to measure the performance efficiencies of Indian police stations is presented

D NUMBERS – FUCOM – FUZZY RAFSI MODEL FOR SELECTING THE GROUP OF CONSTRUCTION MACHINES FOR ENABLING MOBILITY

The paper presents a hybrid model for decision-making support based on D numbers, the FUCOM method and fuzzified RAFSI method, used for solving the selection of the group of construction machines for enabling mobility. By applying D numbers, the input parameters for the calculation of the weight coefficients of the criteria were provided. The calculation of the weight coefficients of the criteria was performed using the FUCOM method. The best alternative was selected using the fuzzified method, which was conditioned by the specificity of the issue so that in this case, the selection of the best alternative was made using the fuzzified RAFSI method

A fuzzy expected value approach under generalized data envelopment analysis

Fuzzy data envelopment analysis (DEA) models emerge as another class of DEA models to account for imprecise inputs and outputs for decision making units (DMUs). Although several approaches for solving fuzzy DEA models have been developed, there are some drawbacks, ranging from the inability to provide satisfactory discrimination power to simplistic numerical examples that handles only triangular fuzzy numbers or symmetrical fuzzy numbers. To address these drawbacks, this paper proposes using the concept of expected value in generalized DEA (GDEA) model. This allows the unification of three models - fuzzy expected CCR, fuzzy expected BCC, and fuzzy expected FDH models - and the ability of these models to handle both symmetrical and asymmetrical fuzzy numbers. We also explored the role of fuzzy GDEA model as a ranking method and compared it to existing super-efficiency evaluation models. Our proposed model is always feasible, while infeasibility problems remain in certain cases under existing super-efficiency models. In order to illustrate the performance of the proposed method, it is first tested using two established numerical examples and compared with the results obtained from alternative methods. A third example on energy dependency among 23 European Union (EU) member countries is further used to validate and describe the efficacy of our approach under asymmetric fuzzy numbers

A novel hybrid fuzzy DEA-Fuzzy MADM method for airlines safety evaluation

Safety is a critical element in the air transport industry. Although fatal air accidents are rare compared to other transport industries, the rapid growth in air travel demands has resulted in a growing aviation risk exposure and new challenges in the aviation sector. Although the issue of airline safety is of serious public concern, notably few studies have investigated the safety efficiency of airlines. This paper aims to propose a novel hybrid method using fuzzy data envelopment analysis (DEA) and fuzzy multi-attribute decision making (F-MADM) for ranking the airlines’ safety. In this study, fuzzy DEA is utilized to calculate criteria weights, in contrast to the conventional approach of using DEA for measuring the efficiency of alternatives. A ranking of each airline (DMU) on the basis of obtained weights is then assessed using MADM methods. Six MADM methods including Fuzzy SAW, Fuzzy TOPSIS, Fuzzy VIKOR, ARAS-F, COPRAS-F and Fuzzy MULTIMOORA are implemented to rank the alternatives, and finally, the results are compounded with the utility interval technique. This new hybrid method can efficiently overcome the pitfalls of traditional hybrid DEA-MADM models. The method proposed in this study is used to evaluate the safety levels of seven Iranian airlines and to select the safest one. © 2018 Elsevier Lt

Carbon efficiency evaluation:an analytical framework using fuzzy DEA

Data Envelopment Analysis (DEA) is a powerful analytical technique for measuring the relative efficiency of alternatives based on their inputs and outputs. The alternatives can be in the form of countries who attempt to enhance their productivity and environmental efficiencies concurrently. However, when desirable outputs such as productivity increases, undesirable outputs increase as well (e.g. carbon emissions), thus making the performance evaluation questionable. In addition, traditional environmental efficiency has been typically measured by crisp input and output (desirable and undesirable). However, the input and output data, such as CO2 emissions, in real-world evaluation problems are often imprecise or ambiguous. This paper proposes a DEA-based framework where the input and output data are characterized by symmetrical and asymmetrical fuzzy numbers. The proposed method allows the environmental evaluation to be assessed at different levels of certainty. The validity of the proposed model has been tested and its usefulness is illustrated using two numerical examples. An application of energy efficiency among 23 European Union (EU) member countries is further presented to show the applicability and efficacy of the proposed approach under asymmetric fuzzy numbers