Intuitionistic fuzzy databases are used to handle imprecise and uncertain data as they represent the membership, nonmembership, and hesitancy associated with a certain element in a set. This paper presents the Intuitionistic Fuzzy Fourth Normal Form to decompose the multivalued dependent data. A technique to determine Intuitionistic Fuzzy multivalued dependencies by working on the closure of dependencies has been proposed. We derive the closure by obtaining all the logically implied dependencies by a set of Intuitionistic Fuzzy multivalued dependencies, i.e., Inference Rules. A complete set of inference rules for the Intuitionistic Fuzzy multivalued dependencies has been given along with the derivation of each rule. These rules help us to compute the dependency closure and we further use the same for defining the Intuitionistic Fuzzy Fourth Normal Form.