Nontraditional manufacturing processes (NTMPs) bring the processing capabilities such as machining high strength and hard materials with desired accuracies and surface finish to the manufacturing companies. Therefore, there has been a significant increase in the use and number of NTMPs. Hence, choosing a particular NTMP for a specific application turns out to be a complex decision-making problem, which involves conflicting qualitative and quantitative ranking criteria. In recent NTMP ranking literature, it is noted that fuzzy approaches are better suited for handling uncertainties and incomplete information that exist within the NTMP ranking environment. This paper introduces such a fuzzy approach using the hesitant fuzzy preference selection index (PSI) method for the assessment of the criteria weights and the hesitant fuzzy correlation coefficient principle for ranking and recommending the most appropriate NTMP for a specific application. The proposed methodology and its efficiency in dealing with incomplete information under the fuzzy decision-making environment are explored with a case study. As a result of the study, the proposed model preferred the electron beam machining (EBM) as the most suitable nontraditional manufacturing process. On the other hand, triangular fuzzy TOPSIS methods offered the electrochemical machining (ECM) as the best choice among the alternatives. The differences among the ranking decisions are also analyzed in the paper. It can be concluded from the authors' various applications of the proposed hesitant fuzzy PSI method that it is extremely effective in representing fuzzy decision-making environments in NTMP ranking decisions.