Schweizer-Sklar T-norm and T-conorm (SSTT), as an important class of the T-norm (TN) and T-conorm (TC), have greater flexibility in the information fusion process, and the Maclaurin symmetric mean (MSM) has a prominent advantage that it can take into account the interrelationships among the multi-input arguments, including multi-attributes or multi-experts in the multi-attribute group decision making (MAGDM), and it is also the generalization of many existing operators. In order to make full use of the advantages of both SSTT and MSM, we extend SSTT to intuitionistic fuzzy numbers (IFNs) and define Schweizer-Sklar operational rules of IFNs. Then, we combine the MSM with Schweizer-Sklar operational rules, and propose the intuitionistic fuzzy Schweizer-Sklar Maclaurin symmetric mean (IFSSMSM) operator, the intuitionistic fuzzy Schweizer-Sklar weighted Maclaurin symmetric mean (IFSSWMSM) operator, respectively. Furthermore, we study some desirable characteristics of them and develop a new method based on these operators to deal with some MAGDM problems. Finally, some examples of practical applications are presented to show the availability and advantages of the proposed method by comparing with some existing methods.