Application of Dempster-Shafer theory in combining the experts’ opinions in DEA

Abstract

In data envelopment analysis models, values of inputs, outputs and their slack weights are usually based on the domain experts’ opinions. While they play a key role in efficiency evaluation of decision-making units in practice, when there are more than one expert, the manager encounters with the problem of effective specification of final values. The problem may be worsen when the belief degree on the opinions is not complete and differs from one expert to the other, which consequently leads to different and sometimes conflicting analytic results. Belief function defined in Dempster–Shafer theory is a powerful tool to derive a possible solution in these circumstances. We adapt this theory to address such situations in data envelopment analysis. A linear optimisation model is devised as a new combination rule of experts’ opinions, which covers the drawbacks of some existing combination rules in the belief function theory. The methodology is visualised with simple examples. Moreover, the well-known Monte Carlo experimentation is used to test the performance of the proposed method.