Exploitation centers are pivotal in multiple industries, especially in the oil and gas sector, contributing significantly to national revenue through exports. The oil and gas extracted are vital to many industrial sectors and end consumers. However, heavy crude oil exploitation and refining operations have undergone substantial changes to meet market demands and comply with environmental regulations. This paper presents a fuzzy network model designed to assess the efficiency of the country's oil and gas exploitation centers, considering undesirable outputs and weak disposability, focusing specifically on the oil exploitation centers of Khuzestan province. Network data envelopment analysis was employed to evaluate the efficiency of these centers, with toxic gases such as CO2 and SO2 identified as undesirable outputs at each stage. The analysis of nine centers revealed that none achieved an efficiency score of one. The primary reasons for this inefficiency were due to the use of outdated equipment resulting from sanctions and the failure to use liquefied and natural gases instead of diesel and gasoline in the machinery used for exploiting and refining crude oil. The model was then extended to the oil exploitation centers of Khuzestan province as a case study, validating its functionality. The results demonstrated the model's ability to effectively evaluate the efficiency of current units. Based on these findings, the adoption of renewable energy and the installation of appropriate filters in the equipment were suggested.