دانلود رایگان مقاله Z-شماره DEA و امکانات جدید DEA در زمینه شماره Z

Abstract

Data envelopment analysis (DEA) is a methodology that uses multiple inputs and outputs for measuring the efficiencies of a set of decision making units (DMUs). When data are crisp, conventional DEA models are used. However the values of inputs and outputs in many cases are imprecise and vague. In addition, most of these data are expert-based. Thus, taking into account expert’s reliability is quite important. In this paper we propose a Z-number version of the CCR (named after Charnes, Cooper, and Rhodes) and BCC (named after Banker, Charnes and Coopers) DEA models. The proposed method can be converted into the fuzzy DEA model when experts are confident about their opinions. Also, it can be converted into the conventional DEA models when the inputs and outputs are crisp numbers. In this study, the Z-number DEA model is transformed into possible linear programming and then by applying an alternative α-cut approach, a crisp linear programming model is obtained. Furthermore, the proposed model is applied to a portfolio selection problem in IS/IT (Information Systems/Information Technology) project to tackle uncertainties, interactions between projects and reliabilities. To the best of our knowledge, this is the first study that presents a unique Z-number DEA model.

6. Conclusions

Presenting data with uncertainty is one of the most important features in most real problems. As stated by Zadeh [6] in his paper: (entitled as ‘‘A note on Z-numbers”) reliability is the inseparable part of uncertainty data in real problems and experts usually represent the data with linguistic variables that is called reliability. In this paper the Z-number version of CCR and BCC DEA models are suggested for vague and incomplete data especially for future analysis of decision making units. We used the concept of Z-numbers for adding the reliability into the fuzziness. We proposed the method for converting these models to possibilistic models and then used the a-cut approach for obtaining equivalent crisp linear programming models. The suggested ranking approach in this paper is an application of fuzzy theory and Z-numbers in DEA. This model is also capable to rank the DMUs that consume Z-number inputs to produce Z-number outputs. We used actual portfolio selection case problem in IS/IT environments to show the applicability of proposed model. We considered the uncertainty, reliability and interactions in the stated case to show how the proposed model can handle such important issues. Table 8 presents the features of the proposed model versus other studies.