RETRACTED: Evaluate teaching quality of physical education using a hybrid multi-criteria decision-making framework (Retracted article. See vol. 20, 2025)

The teaching quality evaluation of physical education is an important measure to promote the professional development of physical teachers, improve the quality of school teaching and personnel training. It is helpful for students to achieve all-round development and better meet the needs of modern talents in the new era. This study aims to establish a novel MCDM (multi-criteria decision-making) framework for evaluating teaching quality of physical education. First, PFNs (picture fuzzy numbers) are suggested to reflect dissimilar attitudes or preferences of decision makers. Then, the typical SWARA (Step-wise Weight Assessment Ratio Analysis) model is modified with PFNs to calculate the weights of evaluation criteria. Considering that some criteria are non-compensatory during the evaluation process, the idea of ELECTRE (elimination and choice translating reality) is introduced to obtain the ranking results of alternatives. Specially, the MAIRCA (Multi-Attribute Ideal-Real Comparative Analysis) method is extended to construct the difference matrix in a picture fuzzy environment. Last, the hybrid MCDM model is utilized to assess the teaching quality of physical education. Its superiority is justified through comparison analyses. Results show that our approach is practicable and can provide instructions for the teaching quality evaluation of physical education.