This work aims to study and observe all the existing score functions that help to rank the single-valued neutrosophic set (SVNS) as well as interval-valued neutrosophic set (IVNS) to make a better choice among all the available alternatives in multi-criteria decision-making (MCDM) problems. An intensive study about all these existing score functions reveals that there holds some limitations in the method of ranking order which is misleading the results in decision-making problems. These observations about the existing score functions of the SVNS and IVNS have been claimed with the help of well-defined examples, illustrating an inefficiency of all these existing score functions. Thus, to propose a valid score function for ranking SVNS and IVNS for making a better selection among all the other available alternatives in MCDM problems is still an open challenging research problem.