Z-number CCR using Trapezoidal Fuzzy Numbers

Abstract

Data envelopment analysis (DEA) is a powerful tool for measuring efficiency of multiple inputs and outputs of a set of decision making units (DMUs). There are several models in DEA such as the Banker, Charnes and Cooper (BCC) model, Andersen and Peterson (AP) model and many more. The data used are normally crisps but in real life, data are usually vague or imprecise such as in real problems that are characterized by linguistic information given by experts. In such cases, the Znumber has been used as it takes into account expert’s reliability on the information given. Currently, the triangular membership function is used in the Z-number CCR model. However, in linguistic assessment the trapezoidal membership function is better suited to capture the vagueness of the assessment. The Znumber CCR model using the trapezoidal membership function for inputs and outputs of a set of DMUs is proposed in this paper. In the present study, the Z-number CCR using trapezoidal membership function is converted into a linear programming model and a crisp linear programming model is obtained by employing α-cut approach,. A numerical example on portfolio selection in Information Systems/Information Technology (IS/IT) is presented to demonstrate the proposed method and to find the best portfolio by ranking them according to their efficiency score.