D-Multi-granular Unbalanced Hesitant Fuzzy Linguistic Term Sets and Their Application to Multiple Attribute Decision Making

It is always challenging for us to process uncertain information. While the proposed multi-granular unbalanced hesitant fuzzy linguistic term set (MGUHFLTS) can handle multi-granular information and the asymmetric distribution of linguistic terms in real decision problems, it treats all hesitant memberships as equally significant, which is clearly inconsistent with reality. To address this deficiency, we introduce a new concept: D-multi-granular unbalanced hesitant fuzzy linguistic term set (D-MGUHFLTS). This concept combines D numbers’ ability to deal with uncertainty with MGUHFLTS’s capability to handle unbalanced and multi-granular linguistic information, enriching the representation of uncertain information. Additionally, we propose comparison rules, operational rules, and aggregation operators of the D-MGUHFLTS. Subsequently, we develop a decision-making method grounded in D-MGUHFLTS and apply it to a real-life scenario pertaining to online doctors’ rankings, showcasing the validity and flexibility of D-MGUHFLTS in processing uncertain information. Furthermore, by comparing it with other methods, we further illustrate the effectiveness and applicability of the proposed method.