Supplier selection is an important process for companies in the plastic sector due to its influence on firm performance and competitiveness. For a proper selection, a number of criteria from different aspects need to be considered by decision makers. Yet, as in different fields, because there are numerous criteria and alternatives to be considered in the plastic industry, choosing an appropriate multicriteria decision‐making approach has become a critical step for selecting suppliers. Therefore, the aim of this research is to define the most suitable supplier of high‐density polyethylene through the integration of powerful multicriteria decision‐making methods. For this purpose, the fuzzy analytic hierarchy process (FAHP) is initially applied to define initial weights of factors and subfactors under uncertainty, followed by the use of decision‐making trial and evaluation laboratory (DEMATEL) to evaluate interrelations between the elements of the hierarchy. Then, after combining FAHP and DEMATEL to calculate the final contributions of both factors and subfactors on the basis of interdependence, the technique for order of preference by similarity to ideal solution is used to assess the supplier alternatives. In addition, this paper also explores the differences between the judgments of decision makers for both AHP and DEMATEL methods. To do these, a case study is presented to demonstrate the validity of the proposed approach.