There is a lot of uncertainty in the data when dealing with the decision making (DMK) problem. The interval valued intuitionistic fuzzy (IVIF) set is a powerful tool to tackle such uncertainties, while the connection number (CN), which is based on the “identity,” “discrepancy,” and “contrary” degrees of the set pair analysis (SPA), the focus of SPA is to study certainties and uncertainties as a system. In the present research, an approach is developed for solving multiple attribute DMK (MADM) problems under IVIF utilizing SPA theory. Firstly, we convert all IVIF values (IVIFVs) into the CNs and then determine their score values. An algorithm is built up to solve an IVIF MADM problem. This algorithm is based on the concepts of mean and variance of each score alternative matrix. Finally, with respect to each alternative, a standard value is calculated to rank the alternatives. To demonstrate the validity and applicability of the current research, several numerical examples are also provided with comparisons of existing approaches. In order to confirm the practicality of the proposed approach, the MADM method is finally used in the application of medical diagnosis.