Compared with large enterprises, the development scale and organizational structure of small and medium-sized enterprises are insufficient, which brings certain limitations to the development of small and medium-sized enterprises in China. In order to promote the long-term development of small and medium-sized enterprises in the new era, it is necessary to require enterprise leaders to innovate marketing plans, strengthen risk management of enterprises, and enhance their strength in market competition. The market risk evaluation of small and medium sized enterprises (SMSEs) in the new era is a multiple-attribute decision-making (MADM). The IVIFSs are employed as the tool for portraying uncertain information during the market risk evaluation of SMSEs in the new era. In this paper, the interval-valued intuitionistic fuzzy (IVIF) Hamacher interactive power geometric (IVIFHIPG) technique is addressed based on IVIF Hamacher interactive weighted geometric (IVIFHIWG) technique and power geometric (PG) technique. Some properties of IVIFHIPG technique were addressed. Then, the IVIFHIPG technique is employed to manage MADM under IVIFSs. Finally, an example for market risk evaluation of SMSEs in the new era is employed to verify the IVIFHIPG technique. Thus, the main contributions of this paper are addressed: (1) the IVIFHIPG technique is addressed based on IVIFHIWG technique and PG technique; (2) the IVIFHIPG technique is came up with to manage the MADM under IVIFSs; (3) a numerical example for market risk evaluation of SMSEs in the new era has been came up with to show the IVIFHIPG technique; and (4) some comparative analysis is addressed to verify the I IVIFHIPG technique.