Fuzzy interpretation of efficiency in data envelopment analysis and its application in a non-discretionary model

Data envelopment analysis (DEA) is a nonparametric model which evaluates the relative efficiencies of decision-making units (DMUs).These DMUs produce multiple outputs by using multiple inputs and the relative efficiency is evaluated using a ratio of total weighted output to total weighted input.In this paper an alternative interpretation of efficiency is first given. The interpretation is based on the fuzzy concept even though the inputs and outputs data are crisp numbers.With the interpretation, a new model for ranking DMUs in DEA is proposed and a new perspective of viewing other DEA models is now made possible.The model is then extended to incorporate situations whereby some inputs or outputs, in a fuzzy sense, are almost discretionary variables

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

Method to defuzzify groups of fuzzy numbers: Allocation problem application

The desertification process converts fuzzy numbers to crisp ones and is an important stage in the implementation of fuzzy systems.In many actual applications, we encounter cases, in which the observed or derived values of the variables are approximate, yet the variables themselves must satisfy a set of relationships dictated by physical principle.When the observed values do not satisfy the relationships, each value is adjusted until they satisfy the relationships among observed data indicating their mathematical dependence on one another.Hence, this study proposes a new method based on the Data Envelopment Analysis (DEA) model to defuzzify groups of fuzzy numbers.It also aims to assume that each observed value is an approximate number (or a fuzzy number) and the true value (crisp value) is found in the production possibility set of the DEA model.The proposed method partitions the fuzzy numbers and the relationships among these observed data are observed as constraints. The paper presents the model, the computational process and applications in a real problem

An improved TOPSIS/EFQM methodology for evaluating the performance of organizations

Studies showed that the scoring system of the EFQM has got some problems that can cause a deviation from the correct assess performance of organization. One of the reasons of this deviation could be due to the scoring approach of EFQM questionnaire. This study is to investigate relationship of each question of the questionnaire with TQM criteria and give a practical way to overcome the existing problem. In this study, with 50 questions of the EFQM and criteria of TQM, a questionnaire has been created. Then, opinions of 175 assessors dealing with EFQM are gathered about the relationship between the questions of EFQM with any of TQM criteria. The data have been processed using SPSS software and the nearest point of a fuzzy number and Topsis model. The results revealed that amount of relationship between each EFQM’s question with TQM criteria isn’t same therefore the weight of each question in EFQM’s questionnaire is not equal to the rest of questions and TQM criteria. Also assigning equal scores to all questions of EFQM’s traditional questionnaire is nonrealistic and consequently, the simplicity additive calculation of assessing performance of organization is also nonrealistic and this is created a deviation to assess properly performance of organization. According to the findings of this study, one should consider the EFQM assessors’ point of view regarding the relationship between criteria of the two models in order to improve organization performance assessments. Finally, considering the level of priority in Topsis method, a relevant scoring system should be created. This can overcome the problem of deviation in assessing the organization’s performance

An enhanced EFQM methodology for evaluating the performance of organization

Previous studies show that traditional scoring system in EFQM model is not robust and is suffering a problem causing deviation in assessing the performance of an organization. This study aims to establish a realistic scoring system and accurate using one of the MCDM methods. AHP method is used in order to consider the effect of interaction EFQM criteria. Moreover, traditional scoring of EFQM model is used in this analysis. Results show that new scoring system is more efficient than the traditional scoring system. This is because that the traditional scoring system of EFQM is based on additive calculations whereas AHP method considers interaction effects of criteria and sub criteria in EFQM model. Also the efficiency and effectiveness of the new scoring system were confirmed by the data obtained from the performance evaluation of 35 organizations in a case study. The integration EFQM and AHP models can create a new scoring system to help prevent the deviation of organization performance assessment