An evaluation method of risk grades for prostate cancer using similarity measure of cubic hesitant fuzzy sets

[Display omitted] •We present a new concept of a cubic hesitant fuzzy set (CHFS).•We propose the generalized distance and similarity measure between CHFSs.•We establish an evaluation method of PC risk grades using the similarity measure.•The 16 actual examples of the PC patients are provided to verify the effectiveness. Prostate cancer (PC) is more common cancer in older men. Then, the existing evaluation method of PC risk grades is based on the AJCC (American Joint Committee on Cancer) staging/scoring system. It utilizes the comprehensive risk data of the prostate-specific antigen (PSA) test, Gleason score, and T2 staging score as the evaluation criteria of PC patients. However, these risk data of PC patients not only may belong to different risk grades simultaneously to result in the unreasonable and uncertain evaluation results to some extent, but also may lose useful fuzzy and uncertain information in the existing evaluation method with non-fuzzy information. To overcome these insufficiencies, the research problems in this study are: (a) to present a new concept of a cubic hesitant fuzzy set (CHFS) for expressing uncertain and hesitant fuzzy information; (b) to propose the generalized distance and similarity measure between CHFSs; (c) to establish a comprehensive evaluation method of PC risk grades with CHFS information by using the similarity measure of CHFSs; and (d) to provide the evaluation examples of PC patients as actual clinical cases for indicating the rationality and effectiveness of the proposed risk evaluation method. Then, the main contribution of this original study is that we present a new concept of CHFS to express uncertain and hesitant information of PC risk grades and the generalized distance-based similarity measure of CHFSs to establish a comprehensive evaluation method of PC risk grades. Finally, by the 16 evaluation examples of the PC patients, all their evaluation results verify the rationality and effectiveness of the proposed comprehensive evaluation method. The comparative analysis demonstrates that its evaluation performance is superior to that of the existing evaluation method of PC risk grades.