Performance evaluation of industry-education integration in higher education from the perspective of coupling coordination-an empirical study based on Chongqing

formula is as follows: UðuiÞ ¼ X n j¼1 lijUðuijÞ ð2Þ In formula (2), U(ui) is called the order degree of the subsystem, U(ui) 2 [0, 1], λij is the weight of the order parameter, and lij � 0; X n j¼1 lij ¼ 1. The greater the order degree of the subsystem is, the higher the orderly development level of the system, and vice versa. Referring to the concept of capacitive coupling and the model of capacity coupling coeffi- cient in physics, the interaction coupling model of multiple systems (or elements) is general- ized. The formula Cn = {(u1 � u2 � . . . � um)/[∏ (ui + uj)]}1/n could represent the coupling degree under multisystem interaction conditions. Therefore, the coupling function of the industrial education composite system can be expressed as C ¼ ½Uðu1Þ � Uðu2Þ�1=2 Uðu1Þ þ Uðu2Þ ð3Þ In formula (3), C is the coupling degree of the industrial education composite system, U(u1) is the order degree of the industrial subsystem, and U(u2) is the order degree of the education subsystem. Obviously, C 2 [0,1], and the greater the value of the coupling degree is, the higher the cou- pling strength. The coupling degree can better reflect the coupling strength between industry and education but cannot reflect the coordination level. Therefore, it is necessary to establish the following coupling coordination function to analyze the coordination degree of interaction coupling between industry and education. D ¼ ðC � TÞ1=2 T ¼ a � Uðu1Þ þ b � Uðu2Þ ( ð4Þ In formula (4), D is the coupling coordination degree, T is the coordination indicator of

industrial education, reflecting the effect and contribution of the comprehensive evaluation index of the two subsystems to their coordination degree, a and b are undetermined coeffi- cients. In the process of coupling coordination development, industrial and education are sup- plementary and indispensable to each other and of equal importance, the coefficient values of this study are a = 0.5 and b = 0.5. The higher the coupling and collaboration degree, the better the system’s coupling and collaboration level. It is best to ensure this, as it can guarantee that the coupling and collaboration degree model reflects both the coupling intensity and collabo- ration level of industry-education integration. 2.2 Indicator system In the 1930s, the Harvard School proposed the famous "Structure-Conduct-Performance" (S-C-P) analytical framework, which deeply analyzed the relationship between structure, con- duct, and performance in the context of industrial competition, becoming one of the most influential analytical paradigms in the theoretical system of industrial economics. According to the S-C-P analytical framework, the basic logic of industrial development should be that during the process of industrial competition and development, the structure of industry deter- mines the conduct of industry, and the conduct of industry in turn determines the perfor- mance of industry [39, 40]. According to this framework, in order to achieve ideal PLOS ONE Performance evaluation of industry-education integration in higher education based on coupling coordination

PLOS ONE | https://doi.org/10.1371/journal.pone.0308572 September 18, 2024 7 / 22