This study intends to identify, analyse, and evaluate sustainability assessment (SA) methods, along with the critical factors of sustainable manufacturing (SM) practice. Based on the opinion of experts and a literature review, 10 SA methods and 20 critical factors of SM practice were identified and analysed in relation to their optimal selection in sustainable operations. This research uses a fuzzy MULTIMOORA (Multi-Objective Optimisation on the basis of a Ratio Analysis plus the full multiplicative form) to rank SA methods based on the weights of the critical factors of SM practice obtained using a fuzzy analytic hierarchy process (AHP). A case study of the leather processing industry in India describes the use of the technique in practice. The ranks obtained using the AHP-fuzzy MULTIMOORA is compared with those obtained using the best–worst method (BWM)-fuzzy MULTIMOORA. The results reveal that the Index of Social Progress and the Social Life Cycle Assessment are the top two reliable SA methods based on the identified critical factors of SM practice. Among the critical factors, the 'identification of alternative raw materials', 'methane mitigation', and 'opting for re-utilisation' are identified as the prominent critical factors of SM practices. In addition to the critical factors of SM, this study also evaluates SA methods as they help to monitor industrial progress towards sustainability. These findings provide useful insights to practitioners and can help them select optimal and robust SA methods. [ABSTRACT FROM AUTHOR]