Stakeholders are increasingly aware of the aspect of sustainability, and the fact that the circular economy facilitates the achievement of sustainable development goals. They place pressure on supply chains to become sustainable, and for this reason, third-party logistics (3PL) service providers, as specialized professionals, play a vital role in sustainable supply chain management. Although developments in technology in the era of Industry 4.0 have been effective at directing 3PLs along the path towards sustainability, integrated management of forward and reverse logistics systems in order to achieve a circular economy and to become sustainable remains a problem, even in developed countries. However, benchmarking and using the experiences of others can help to speed up this path at a minimal cost. An interval type-2 fuzzy super-slack-based measure network DEA was developed to make such benchmarking possible. Governance style, staff behavior, environmental management systems, and social elements are considered, alongside the principles of the circular economy, in order to compare the sustainability performance of 17 3PLs with respect to different aspects through the application of the developed DEA model. Proper benchmarking with respect to strategies and operations of the 3PLs that are recognized as efficient makes it possible for these 3PLs to overcome obstacles and progress at a lower cost. The results show that 3PLs do not have a comprehensive sustainability strategy that is coordinated with an overall vision of the total supply chain. An investigation into the development of a framework with multiple steps for the guidance of 3PLs, as well as the whole supply chain, towards sustainability in the Industry 4.0 era would be a fruitful next study.