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Data envelopment analysis (DEA), as a well-established nonparametric method, is used to meet efficiency evaluation purposes in many businesses, organizations, and decision units. This paper aims to present a novel integrated approach to fuzzy interpretive structural modeling (FISM) and dynamic network data envelopment analysis (DNDEA) for the selection and ranking of sustainable suppliers. First, suppliers' efficiency values in a supply chain are determined, using the dynamic network data envelopment analysis (DNDEA) model developed for this purpose. Then, a heuristic method is presented based on the fuzzy interpretive structural modeling (FISM) to find a common set of weights (CSWs) for the variables involved. Depending on the data conditions, two approaches, viz. centralized and decentralized, are proposed for efficiency measurement. To illustrate the model's capability, the proposed methodology is further applied to the real data of a company, named Nirou Moharekeh Industries (NMI). The results of a study on 12 suppliers within the DNDEA model accordingly reveal that one unit (i.e. KARAN) obtains an efficient value, but an inefficient score is observed in 11 units, whose technical efficiency value is in the range of 0.6409 to 0.9983. After utilizing the weights gained from the heuristic method, the efficiency value of the most inefficient supplier (that is, SIRINS.N.) dwindles from 0.6409 to 0.6319.