Similarity measure with indeterminate parameters regarding cubic hesitant neutrosophic numbers and its risk grade assessment approach for prostate cancer patients

Abstract

The prostate cancer (PC) of older men has become an important problem with the increment of aging degree in current society. Then, it is necessary to give the timely detection and reasonable risk assessment of a PC patient so as to provide a suitable treatment option for the PC patient. However, there may exist the hybrid information of an interval-valued fuzzy number (IVFN) and a hesitant indeterminate number/hesitant neutrosophic number (HNN) together in risk data of PC patients, while existing PC risk grade assessment approaches with the cubic hesitant fuzzy set (CHFS) composed of an IVFN and a hesitant fuzzy set cannot carry out such a risk grade assessment problem with the hybrid information of both IVFN and HNN. To solve the issue, for the first time this study proposes a cubic hesitant neutrosophic number (CHNN) to express the hybrid information of both IVFN and HNN and then introduces a similarity measure with an indeterminate parameter regarding CHNNs for the risk grade assessment of PC patients. In this paper, therefore, a concept of a CHNN set is firstly presented to suitably express the hybrid information of both IVFN and HNN as the generalization of CHFS. Then, the CHNN set is transformed into the parameterized CHFS (P-CHFS) for de-neutrosophication by means of an indeterminate parameter. Next, generalized distance and similarity measures between P-CHFSs are proposed based on the least common multiple cardinality/number (LCMC) extension method. Thus, a PC risk assessment approach is developed by using the similarity measure of P-CHFSs with the physician’s optimistic, moderate and pessimistic attitudes under CHNN environment. Finally, sixteen clinical cases are provided as risk assessment examples of PC patients to indicate the effectiveness and applicability of the proposed PC risk assessment approach in CHNN setting. However, the proposed assessment approach can effectively and flexibly deal with assessment problems of PC risk grades regarding the physicians’ optimistic, moderate and pessimistic attitudes in CHNN setting, which shows its advantage.