This paper presents an overview of the existing notions of Bags, Fuzzy Bags, IC-Bags, IF-Bags and Fuzzy IC-Bags. Based on these notions, the concept of Intuitionistic Fuzzy Bags with Interval Counts (Intuitionistic fuzzy IC-Bags) is proposed. Further, some characteristics of Intuitionistic fuzzy IC-Bags are studied, and some examples are furnished in this context.