Comprehensive analysis using triangular fuzzy neutrosophic MADM and grey relational techniques with teaching quality evaluation

The quantification of evaluation indicators for the quality of university physical education classroom teaching is the main development trend of the current evaluation system, which can to some extent avoid the drawbacks caused by subjective blindness and more objectively and scientifically evaluate the quality of university physical education classroom teaching. However, physical education teaching is a complex overall activity, and its characteristics and elements cannot be fully evaluated through quantitative indicators. Therefore, excessive pursuit of quantification in order to make the evaluation indicators more convenient and operable cannot guarantee the effectiveness and accuracy of the evaluation. The classroom teaching quality evaluation of College Physical Education is viewed as the multi-attribute decision-making (MADM). In this paper, the triangular fuzzy neutrosophic numbers grey relational analysis (TFNN-GRA) method is built based on traditional grey relational analysis (GRA) and triangular fuzzy neutrosophic sets (TFNSs). Firstly, the TFNSs is introduced. Then, combine the traditional fuzzy GRA model with TFNSs information, the TFNN-GRA method is established and the computing steps for MADM are built with completely unknown weight information. Finally, a numerical example for classroom teaching quality evaluation of College Physical Education has been given and some comparisons is used to proof advantages of TFNN-GRA method. The main contributions of this paper are listed (1) A novel TFNN-GRA method is proposed to solve the MADM with completely unknown weight information; (2) an optimization model is constructed to obtain a simple formula which could be employed to construct the attribute weights values based on the Lagrange function; (3) a numerical example for classroom teaching quality evaluation of college physical education is constructed to verify the TFNN-GRA method.