Investigation of physical education classroom teaching using AHP with IV-CIFS-based aggregation operators

Assessing physical education (PE) classroom teaching enhancement through modern technologies remains a difficult task in the present era. The evaluation system contains four fundamental dimensions: student engagement, skill development effectiveness, cognitive impact, and feedback and assessment capability. Multi-attribute decision-making (MADM) is one of the most trending systems for ranking alternatives based on their attributes. The interval-valued circular intuitionistic fuzzy set is an advanced approach for assessing MADM problems, rather than the existing simple circular intuitionistic fuzzy set. The ordinary circular intuitionistic fuzzy set lacks a concept of intervals in membership degree (MD), non-membership degree (NMD), and circular degree (CD), resulting in a significant amount of information being lost. Dombi operations are a valuable approach to improving the precision of aggregated results. The interval-valued circular intuitionistic fuzzy set-based analytic hierarchy process (AHP) provides a structured and objective framework for evaluating various innovative teaching approaches, which can be complex. The evaluation process utilizes interval-valued circular intuitionistic fuzzy set-based AHP to assess three innovative PE teaching methods that help educators and policymakers maximize the effectiveness of their instruction. In the past, various approaches were defined within different fuzzy set-based frameworks; however, they lacked a proper method for evaluating the weightage of alternatives. There is a need to define new concepts using interval-valued circular intuitionistic fuzzy set-based information under AHP for the assessment of vague and uncertain MADM problems. By applying the concept of AHP, Dombi operations, and interval-valued circular intuitionistic fuzzy set, this study develops new theories, including interval-valued circular intuitionistic fuzzy Dombi weighted averaging (IV-CIFDWA) and interval-valued circular intuitionistic fuzzy Dombi weighted geometric (IV-CIFDWG) aggregation operators (AOs). The presence of AHP in the proposed approach makes it unique from other existing MADM approaches. We also investigate some desirable axioms of AOs. We offer an MADM algorithm based on a theory developed for precisely investigating fuzzy information. Solve the numerical problem of selecting the best PE platform using the MADM approach. We are ranking the set of considered alternatives like use of wearable fitness technology; game-based learning technology; video Feedback and performance analysis; task-based cooperative Learning. We noticed that use of wearable fitness technology is the best alternative is achieved by using the IV-CIFDWA and IV-CIFDWG operators. We compare our proposed methods with existing methods to verify their authenticity and accuracy. Lastly, we offer a conclusion.