A modified TOPSIS and generalized Hamacher Heronian mean aggregation operator incorporating bipolar Pythagorean Neutrosophic sets and their applications

Amongst complex and data-driven systems, Multi-Criteria Decision-Making (MCDM) models like Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) have several limitations, including a heavy reliance on distance-based calculations and conventional aggregation procedures, which may not adequately capture complex relationships among criteria or effectively represent uncertainty, bipolarity, and indeterminacy in expert evaluations. To address these limitations, this study extends the TOPSIS framework by proposing the Adaptive Ranking with Ideal Evaluation (ARIE) method, which retains the ideal-solution concept but introduces a new evaluation and ranking mechanism. To enhance its ability to handle uncertainty, Bipolar Pythagorean Neutrosophic Generalized Hamacher Heronian Mean (BPN-GHHM) and its weighted extension, BPN-GWHHM operators are introduced. These operators are supported by two BPNS linguistic scales to represent positive, negative and indeterminate judgments. The proposed frameworks are applied to evaluate English vocabulary learning strategies in higher education. Results show that gamification-based learning strategies emerge as the most effective approach for improving English language learning outcomes. Thus, the proposed framework produces consistent results and effectively handles uncertainty and complex relationships among evaluation criteria in educational decision-making contexts. Future studies are recommended to apply the framework to larger datasets and other domains.