This paper presents a fuzzy multicriteria group decision making approach for evaluating the performance of Cloud services in a hesitant fuzzy environment. To model the inherent subjectiveness and imprecision of the performance evaluation process, interval-valued intuitionistic fuzzy numbers are used. An effective algorithm is developed based on the technique for order preference by similarity to ideal solution (TOPSIS) method and Choquet integral operator for dealing with the Cloud services performance evaluation problem. An example is presented to demonstrate the applicability of the proposed fuzzy multicriteria group decision making approach for solving the multicriteria group decision making problem in real world situations.