Building a sustainable transportation system without involving international oil companies (IOCs) is an unrealistic feat. To date, no study has determined the best IOC and low-performing ones with respect to sustainable oil transportation, which is considered a benchmarking challenge requiring an urgent solution. Despite this limitation, the benchmarking of IOCs falls under the complex multi-criteria decision making (MCDM) because of the use of several evaluation criteria and their varying datasets and the varying importance of these criteria. Moreover, the issues involving the use of imprecise, unclear and ambiguous information remain unresolved in the existing multi-attribute decision-making methods. The robustness of the multi-objective optimisation on the basis of ratio analysis (MULTIMOORA, i.e. an updated version of MOORA) plus full-multiplicative form (FMF) method and that of the fuzzy-weighted with zero inconsistency (FWZIC) method have been proven. Therefore, in this study, we propose a novel benchmarking of oil companies by extending the linear Diophantine fuzzy rough sets (LDFRSs) into the MCDM methods to help build a sustainable transportation industry. The proposed methodology consists of two phases. The initial phase involves assigning values to the evaluation criteria of IOCs to formulate the evaluation decision matrix. The second phase involves the development of two fuzzy MCDM methods, namely, the LDFRS with the FWZIC method (hereafter called LDFRS–FWZIC) for weighting the criterion of each IOC and the LDFRS with the MULTIMOORA method (hereafter called LDFRS–MULTIMOORA) for benchmarking the IOCs. The IOCs were evaluated based on 2 criteria, 9 sub-criteria and 47 measurement items by 483 experts from 11 IOCs. Results revealed the following: (i) LDFRS–FWZIC can effectively weigh the evaluation criteria of IOCs. The highest final weight of 0.2594 was for ‘cost leadership’ (C2-1), whereas the lowest weights of 0.1148 was for ‘priority of other external matters’ (C1-2) and ‘insufficient supply’(C1-4). (ii) LDFRS–MULTIMOORA can successfully benchmark the IOCs. IOC11 ranked first, followed by IOC10 and IOC3 in the second and third ranks, respectively. IOC4 ranked the lowest (<italic>rank = 11</italic>). A sensitivity analysis was conducted to determine the robustness of the developed fuzzy MCDM methods.