Fostering Linguistic Decision-Making under Uncertainty: A Proportional Interval Type-2 Hesitant Fuzzy TOPSIS Approach Based on Hamacher Aggregation Operators and Andness Optimization Models

•The notion of PIT2 HFS and its operational laws and serval measures were defined.•The Ham-PIT2HFPWA and Ham-PIT2HFPWG operators were proposed for PIT2 HFEs.•Two andness optimization models were constructed for aggregation parameter determination.•The algorithm of transforming GCLEs into PHFLTSs, and further PHFLTSs into PIT2 HFEs was designed.