The use of fuzzy sets, intuitionistic fuzzy sets and neutrosophic sets can often handle with real-life problems that contain incomplete and uncertain information. The 0-1 scale is used to deal with such information which is graded symmetrically and uniformly but, some problems consist of unsymmetrical and non-uniform information. Although intuitionistic multiplicative set (IMS) is a powerful tool to deal with this kind of problems, due to the dependence of hesitant information to the membership and non-membership functions in IMS, it brings a restriction to decision-makers while working on the real-life problems such as applications of correlation coefficients and clustering. In this study, we propose novel correlation coefficients (CCs) of simplified neutrosophic multiplicative sets (SNMSs) which is defined recently by removing the shortages of IMSs. Firstly, we give SNMS-based operations, fulfil the deficiencies in the theoretical background of IMS and establish a theoretical structure for the SNMS. Then, we propose novel correlation coefficients (CC) of SNMS and show some of their important properties. Finally, we apply the CCs to a clustering problem to confirm the efficiency of the proposed SNMS and its correlation coefficients.