Z-number DEA: A new possibilistic DEA in the context of Z-numbers

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.