Application of Fuzzy Data Envelopment Analysis in Decision Making

Nowadays, financial institutions are considered as a main economy foundations in all of the countries that their economic flourish is depend on such institutions. The banks as a financial basis play important role in the economy. But in developing countries financial and monetary markets have the first role in provision of long and medium-terms. So, it is necessary to use suitable criteria for banks efficiency probing. We know that Fuzzy data envelopment analysis (FDEA) by evaluating their relative efficiency is a widely used mathematical programming that compares the inputs and outputs of a set of decision-making units (DMUs). According to the available information, thirty branches of Maskan banks in northwest of Tehran have chosen as a sample. Then, they were examined by use of the model presented in this paper.

Expert Systems with Applications, 2014

Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision making units (DMUs) with multiple inputs and multiple outputs. However, in real life applications, undesirable outputs may be present in the production process which needs to be minimized. The present study endeavors to propose a DEA model with undesirable outputs and further to extend it in fuzzy environment in view of the fact that input/output data are not always available in exact form in real life problems. We propose a fuzzy DEA model with undesirable fuzzy outputs which can be solved as crisp linear program for each a in (0, 1] using a-cut approach. Further, cross-efficiency technique is applied to increase the discrimination power of the proposed models and to rank the efficient DMUs at every a in (0, 1]. Moreover, for better understanding of the proposed methodology, we present a numerical illustration followed by an application to the banking sector in India. This is the first study which attempts to measure the performance of public sector banks (PuSBs) in India using fuzzy input/ output data for the period 2009-2011. The results obtained from the proposed methodology not only depict the impact of undesirable output on the performance of PuSBs but also analyze efficiently the influence of the presence of uncertainty in the data over the efficiency results. The findings show that the efficiency results of many PuSBs vary with the variation in a during the selected period.

Research Square (Research Square), 2022

Fuzzy data envelopment analysis (FDEA) is an efficient modeling technique to rank decision-making units (DMUs) with imprecise inputs/outputs. It is a linear programming problem that constructs an optimal frontier line, known as an efficient frontier. The role of the efficient frontier is to distinguish between the efficient DMUs with inefficient DMUs such that all efficient DMUs lie on the frontier line. Whereas the inefficient DMUs are enveloped by the frontier line. This optimization problem aims to improve the efficiency score of each inefficient DMU, that is, to move them to the efficient frontier. In this study, we propose a novel approach called the Pythagorean approach, which is both input and output oriented. The proposed approach is implemented in the CCR model, and a new version of the BCC model is introduced, namely a novel Pythagorean BCC model. The deterministic form of the Pythagorean BCC model is extended to a fuzzy environment to deal with the vagueness of the given dataset. In the paper, a new form of a non-linear fuzzy number, namely a sine-shaped fuzzy number, has been introduced to display the higher order of uncertainty. Consequently, the Pythagorean BCC model is further extended to a novel Pythagorean fuzzy BCC model. The model's efficacy is finally tested in the Indian public sector banks.

Economic Modelling, 2013

In the fast changing financial circumstances of nowadays, in avoiding the crisis of closing down, financial institutions are concerned about the efficiency and risk strictly in the meantime. Therefore, efficiency and risk management are goals for a financial institution administrator. Data Envelopment Analysis (DEA) is a non-parameter approach to evaluate the performance of DMU's efficiency and the variables used in the DEA are all accurate values. However, when the input or output variables are fuzzy, the performance of DMUs must proceed by the Fuzzy-DEA. On the basis of risk uncertainty, this research plans to apply the expanding model of Fuzzy Slack-Based Measurement (Fuzzy SBM). The efficiency scores estimated by Fuzzy SBM model are subordinate to functional form, which provides efficiency value region in different degrees of confidence, conforms to the characteristic of risk anticipation, and estimates the management achievement of Taiwan banking under market risk.

Expert Systems with Applications, 2013

Data envelopment analysis (DEA) is a linear programming based non-parametric technique for evaluating the relative efficiency of homogeneous decision making units (DMUs) on the basis of multiple inputs and multiple outputs. There exist radial and non-radial models in DEA. Radial models only deal with proportional changes of inputs/outputs and neglect the input/output slacks. On the other hand, non-radial models directly deal with the input/output slacks. The slack-based measure (SBM) model is a non-radial model in which the SBM efficiency can be decomposed into radial, scale and mix-efficiency. The mixefficiency is a measure to estimate how well the set of inputs are used (or outputs are produced) together. The conventional mix-efficiency measure requires crisp data which may not always be available in real world applications. In real world problems, data may be imprecise or fuzzy. In this paper, we propose (i) a concept of fuzzy input mix-efficiency and evaluate the fuzzy input mix-efficiency using a -cut approach, (ii) a fuzzy correlation coefficient method using expected value approach which calculates the expected intervals and expected values of fuzzy correlation coefficients between fuzzy inputs and fuzzy outputs, and (iii) a new method for ranking the DMUs on the basis of fuzzy input mix-efficiency. The proposed approaches are then applied to the State Bank of Patiala in the Punjab state of India with districts as the DMUs. j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e s w a SBM model (FSBM I ) with fuzzy input and fuzzy output data. Several approaches have been developed to deal with imprecise or fuzzy data in DEA. Sengupta (1992) applied principle of fuzzy set theory to introduce fuzziness in the objective function and the right-hand side vector of the conventional DEA model. Guo and Tanaka (2001) used the ranking method and introduced a bi-level programming model. Lertworasirikul (2001) developed a method in which the inputs and outputs were firstly defuzzified and then the model was solved using a-cut approach. There are some other approaches based on a-cut which can be found in Meada, Entani, and Tanaka () transformed fuzzy input and fuzzy output into intervals by using a-level sets and built a family of crisp DEA models for the intervals. Liu (2008) and Liu and Chuang (2009) developed a fuzzy DEA/AR model for the selection of flexible manufacturing systems and the assessment of university libraries respectively. proposed a generalized fuzzy data envelopment model with assurance regions, whose lower and upper bounds at given levels could be obtained. and also changed fuzzy input and fuzzy output data into intervals by usinga-level sets, but suggested two different interval DEA models. Dia proposed a FDEA model based on fuzzy arithmetic operations and fuzzy comparisons between fuzzy numbers. The model requires the decision maker to specify a fuzzy aspiration level and a safety a-level so that

Fuzzy Sets and Systems, 2003

Evaluating the performance of activities or organizations by traditional data envelopment analysis (DEA) models requires crisp input/output data. However, in real-world problems inputs and outputs are often imprecise. This paper develops DEA models using imprecise data represented by fuzzy sets (i.e., "fuzzy DEA" models). It is shown that fuzzy DEA models take the form of fuzzy linear programming which typically are solved with the aid of some methods to rank fuzzy sets. As an alternative, a possibility approach is introduced in which constraints are treated as fuzzy events. The approach transforms fuzzy DEA models into possibility DEA models by using possibility measures of fuzzy events (fuzzy constraints). We show that for the special case, in which fuzzy membership functions of fuzzy data are of trapezoidal types, possibility DEA models become linear programming models. A numerical experiment is used to illustrate the approach and compare the results with those obtained with alternative approaches.

Expert Systems with Applications, 2015

Intuitionistic fuzzy set (IFS) is an extension of fuzzy set and an approach to define a fuzzy set where available information is not sufficient to define an imprecise concept by means of a conventional fuzzy set. The existing fuzzy DEA (FDEA) models for measuring relative fuzzy efficiencies of decision making units (DMUs) are limited to fuzzy input/output data. However, in real life applications, some inputs and outputs of subjective, linguistic and vague forms may possess intuitionistic fuzzy essence instead of fuzziness. Therefore, in the present study, we extend FDEA to intuitionistic fuzzy DEA (IFDEA) in which the input/output data are represented by intuitionistic fuzzy numbers (IFNs), in particular triangular IFNs (TIFNs). This is the first study in analysing optimistic and pessimistic efficiencies with intuitionistic fuzzy input/output data in DEA. In this study, we develop models to measure optimistic and pessimistic efficiencies of each DMU in intuitionistic fuzzy environment (IFE). By using super-efficiency technique, we develop algorithms to obtain the complete ranking of the DMUs when optimistic and pessimistic situations are considered separately. Further, to rank the DMUs when both optimistic and pessimistic situations are taken simultaneously as hybrid approach, we propose two alternate ranking methods based on levels of inefficiencies and efficiencies respectively. To address the overall performance using optimistic and pessimistic situations together in IFEs, we propose a hybrid IFDEA performance decision model. To validate the proposed methodology and proposed ranking methods, we illustrate different numerical examples and then compare the results with an existing ranking approach based on geometric average efficiency index. Moreover, we present an application of the proposed approach to the banking sector in which two inputs, namely, labour and operating expenses possess intuitionistic fuzzy essence at branch level, and are represented as TIFNs.

In today's economy and society, performance analyses in the services industries attract more and more attention. The traditional data envelopment analysis (DEA) approach requires a consistent operating environment. However, in reality, there is a need to evaluate the units belonging to different environment. This reality challenges the traditional methods of applying DEA theory to real-world cases where benchmarking across region can be a very important undertaking. This paper introduces the fuzzy logic into DEA formulation to deal with the environmental variables so that the performance of bank branches from different regions can be assessed. The inner-province and inter-province comparison are given based on the fuzzy DEA results. These results are also compared with the results from traditional DEA analysis.

Journal of Namibian Studies : History Politics Culture

Performance assessment is a central to the management process in any type of organization. In addition, making rational economical decisions to improve organizational performance is a daunting task, as any organization is typically a multi-faceted entity which rely on complex systems that use uncertain information. Data envelopment analysis (DEA) is a powerful quantitative tool that makes use of multiple inputs and outputs to obtain useful information about the performance and efficiency of an organization. In many real-life applications, observations are usually fuzzy in nature. Therefore, DEA efficiency measurement may be sensitive to such variations. The purpose of this study is to develop a unified economical fuzzy DEA model that handles variables of different natures (vague and deterministic) independently and can be adapted to both input- and output-oriented problems, whether it is constant/variable return to scale. To handle fuzzy variables specially the economic variables in...

Routledge, 2024

Westra explores a nuanced literature on post-capitalism which claims that instead of constituting the end of history or ending in its supplanting by socialism, capitalism has transmuted into something else. Foci of this literature ranges from questions of financial system and technological change through evidence of shifting class contours metastasizing a more predatory constellation. In exposing the dire consequences for humanity of capitalist unravelling, Westra remedies the lacunae of current writings which leave fundamental questions of what precisely capitalism is or was and the historical delimitations of capitalism unanswered. He not only critically analyzes the arguments over capitalisms passing under key rubrics of financialization, globalization, intangible assets and social class, but grounds determinations over the existence of capitalism in a novel synthetic definition of it drawn from Marx. While capitalism has always been an exploitative, asymmetric wealth distributive, alienating, class divisive, crises ridden society, Westra explains how current economic transmutations undermine what coherence capitalism had historically maintained. This book, written in a clear and compelling fashion, is a clarion call for social change. It will be of interest to academics and students across fields of economics, political economy, economic history, political science and sociology as well as to progressive policymakers and social activists.