The Dice measure of cubic hesitant fuzzy sets and its initial evaluation method of benign prostatic hyperplasia symptoms.

In order to give the initial evaluation of benign prostatic hyperplasia (BPH) symptoms regarding a patient, physician usually performs the clinical inquiry of the patient, whereas his/her responses may contain hesitant fuzzy and uncertain information. However, existing evaluation/diagnosis approaches of BPH symptoms cannot cope with the hybrid problem of both hesitant and uncertain responses of patients. Furthermore, existing evaluation approaches may lose some useful responses (e.g. hesitant fuzzy information) so as to result in the unreasonable or indeterminate evaluation/diagnosis in the evaluation process of patients. To overcome this insufficiency, this study firstly introduces the concept of a cubic hesitant fuzzy set (CHFS) based on combining uncertain/interval-valued fuzzy information with hesitant fuzzy information so as to express the hybrid fuzzy information and proposes the Dice measure between CHFSs based on the extension method of the least common multiple cardinality/number (LCMC) for the hesitant fuzzy sets in CHFS. Then, the initial evaluation approach of BPH symptoms is developed by using the Dice measure of CHFSs. Lastly, the assessment results of six BPH patients are presented as the clinical actual cases to indicate the applicability and effectiveness of the developed assessment approach in CHFS setting. The comparison with existing common evaluation methods shows that the developed evaluation/diagnosis method is superior to the existing common evaluation methods in the evaluation/diagnosis process of the clinical actual cases.