Mahalanobis distance-based grey correlation analysis method for MADM under q-Rung orthopair hesitant fuzzy information on the lung cancer screening

The implementation of early screening methods holds considerable importance in enhancing the early identification and survival rates associated with lung cancer. Due to the uncertainty of early lung cancer identification, psychological factors of experts and changes in specific symptoms make experts hesitant and vague in their diagnosing judgment. Therefore, Early lung cancer screening can be seen as a fuzzy multi-attribute decisionmaking(MADM) problem characterized by uncertainty and ambiguity. However, faced with complex early lung cancer screening under hesitant and ambiguous information, existing fuzzy decision-making methods ignore the potential correlation of symptom characteristics, the psychological factors of experts in diagnostic evaluation are not considered, and generate a large amount of redundant data resulting in low computational efficiency. To this end, firstly, the notion of fuzzy dispersion degree is introduced in this paper and is used to assess the membership and non-membership degrees divergence information of a q-rung orthopair hesitant fuzzy number. On this basis, the covariance matrix formula and a novel Mahalanobis distance for q-ROHFS are derived, which can thoroughly investigate the potential fuzzy correlations of symptom characteristics evaluated by experts from a statistical analysis perspective and make up for the defects of existing fuzzy distances that suffer from data redundancy. Secondly, combining the proposed Mahalanobis distance and regret theory, a grey correlation analysis MADM method is developed. The feasibility of the proposed method is demonstrated through a case study of a regional hospital expert to perform early lung cancer screening. Finally, the rationality and efficiency of the proposed method are verified through comprehensive comparative analysis, which shows that the proposed method considers expert psychological behavior and attribute correlation while avoiding data redundancy and enhancing computational efficiency.