In this study, we combine an interval type-2 fuzzy best-worst method (IT2FBWM) with the interval VIKOR method for the first time to evaluate and prioritize sustainable suppliers in circular supply chains. To weigh the criteria, an interval type-2 best worst approach is employed, and the interval VIKOR methodology is utilized to assess the suppliers in the presence of uncertainty. Risk is presented in all supply chain activities, and its occurrence affects all dimensions of the supply chain and can cause damage to them and, therefore, must be appropriately managed. A new mixed-integer linear programming model is then formulated to identify each risk's optimal strategy or response. The multi-objective model minimizes total costs and response time and maximizes risk responses to secondary and primary risks. An improved version of augmented ε-constraint method (AUGMECON2) is also employed to produce separate Pareto-optimal solutions. Finally, the suggested strategy is applied to four main suppliers in the food company. The findings of the proposed integrated approach demonstrate the applicability and efficiency in the food industry.