A novel simplified yielded aggregation index (SYAI) method integrated with hesitant triangular fuzzy generalized geometric heronian mean for enhanced MCDM

This study addresses the problem of decision-making under linguistic uncertainty, expert hesitation, and interrelated criteria in Multi Criteria Decision Making (MCDM). Existing MCDM methods often assume precise numerical data and mainly focus on benefit and cost criteria, while limited attention is given to hesitant triangular fuzzy information and goal-type criteria. To overcome these issues, this study proposes the Simplified Yielded Aggregation Index (SYAI) integrated with the Hesitant Triangular Fuzzy Generalized Geometric Heronian Mean (HTFGGHM) operator. The novelty of the proposed SYAI-HTFGGHM framework lies in its ability to combine a unified normalization structure for benefit, cost, and goal-type criteria with a hesitant triangular fuzzy aggregation operator that captures inter-criteria relationships. The mathematical properties of the HTFGGHM operator, including idempotency, monotonicity, and boundedness, are established to support its theoretical validity. The proposed framework is applied to evaluate humor-based teaching strategies in Arabic language learning at UiTM using expert evaluations from five Arabic language lecturers. The results show that verbal humor (A1) is the most preferred strategy, followed by non-verbal humor (A2), situational humor (A4), and technology-based humor (A3). Comparative analysis with TOPSIS, VIKOR, SAW, COBRA, WASPAS, and MOORA further confirms the consistency of the ranking results. Overall, the proposed SYAI-HTFGGHM framework provides a transparent and practical MCDM approach for handling hesitant linguistic evaluations, interrelated criteria, and mixed criterion types in uncertain decision making environments.