Summary: A cubic soft set (CSS) is a combination of an interval-valued fuzzy set (IVFS) and a fuzzy set (FS). Cubic soft matrix (CSM) plays a significant role in analyzing modern uncertainty. In this manuscript, we discuss two novel approaches using a real-life scenario. One being, to use the combination of IVFS and FS and the other, to find a unique ranking using parameters. First, we introduce some basic operations of ‘OR’, ‘AND’, and complement of CSM. Second, we propose the concept of a weighted fuzzy vector (WFV), weighted interval-valued fuzzy vector (WIVFV), weighted cubic vector (WCV) and construction of cubic matrices to solve multi-criteria decision making (MCDM) problems. Third, we discuss the concept of the value and the score function to rank the alternatives and choose the best one. Finally, we present an MCDM problem to deal with the selection of a suitable candidate for a specific job in an organization with two case studies to illustrate the working and reliability of the proposed model.