In the Network data envelopment analysis, in addition to external inputs and outputs of a decision-making unit, interactions between internal subprocesses are also respected. These interactions could be an essential part of an efficiency assessment of decision-making units, while in many circumstances, they are represented as undetermined quantitative values by the experts of the domain. Uncertainty theory, initiated in 2007 and then completed in 2009, is an axiomatic mathematical framework for formalizing human reasoning. Here, we consider the network DEA at which both external and internal data are provided by an expert and design a novel procedure in the efficiency evaluation process of decision-making units using the uncertainty theory. We consider the basic model for a typical small instance, and a crisp counterpart is provided. The presented numerical example could be evidence of the applicability of the methodology in practice.