Modeling College English Teaching Quality Evaluation Using Induced Interval-Valued Intuitionistic Fuzzy Hamacher Interactive Operator

College English course instruction mainly covers content that includes language knowledge and practical skills, and it is also a primary avenue for enhancing students' English learning strategies and intercultural communication competence. The college English teaching quality evaluation is a multi-attribute decision making (MADM). This paper approaches college English teaching quality assessment as a MADM process. Fundamental computational rules for interval-valued intuitionistic fuzzy sets are presented, including the Hamacher sum and product operations. A novel aggregation tool, termed the induced interval-valued intuitionistic fuzzy Hamacher interactive ordered weighted averaging operator, is developed and its desirable mathematical properties are thoroughly examined. The proposed operator is then applied to solve MADM problems within the framework of interval-valued intuitionistic fuzzy sets. To validate its practical utility, a detailed case study on evaluating college English teaching quality is conducted using this new methodology.