The supply chain network design problem addresses various factors that maximize customers' demand and minimizes the sum of strategic, tactical, and operational costs. Companies with common activities in their supply chains have started to cooperate with each other to achieve better service levels. Based on this initiative, a multi-level mixed-integer linear programming model is developed that includes two allied supply chains with different decision makers (DM) at two different decision-making levels. The primary aim of this study is to design an allied closed-loop supply chain (CLSC) network that uses some of the same facilities. The secondary aim of this study is to examine this allied CLSC model simultaneously and analyse the impact of the DMs' objectives based on satisfaction degrees. Various interactive fuzzy programming (IFP) approaches were utilized to examine the presented multi-level CLSC model. A novel IFP approach which is based on the fuzzy analytic hierarchy process (AHP) is proposed. The effectiveness of the proposed IFP approach on the CLSC model is investigated with hypothetical data. The computational results show that the proposed approach obtains higher satisfaction degrees for upper-level DMs than the other approaches.