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

(1) Performance and development trend of the education and production subsystem. The upper and lower limits of each order parameter increase or decrease by 5% respectively on the basis of the actual maximum or minimum value, and the above model is used to calculate the order parameter efficacy coefficient and subsystem order. According to synergism, the effi- cacy coefficient represents the contribution of order parameters to the orderly development of subsystems. The greater its value, the greater its contribution, and the higher the degree of orderly development, and vice versa. From the calculation results, it can be found that from 2000 to 2022, the order degree of Chongqing’s industrial subsystem and education subsystem increased steadily, and the overall trend was upward, which promoted the orderly develop- ment of the two subsystems. as shown in Table 4. Overall, during the period from 2000 to 2022, the orderliness degree of the industrial sub- system educational subsystem in Chongqing’s industry-education composite system contin- ued to rise alternately, which also jointly determined the continuous increase in the synergy of the composite system. From 2000 to 2022, the orderliness curves of the industrial and educa- tional subsystems have been continuously rising alternately, indicating that the overall level of orderly development of industry and education in Chongqing is constantly improving. Among them, the orderliness of industrial development has increased from 0.2151 in 2000 to

0.6928 in 2022, with a significant increase in orderliness. The order degree of higher education has increased from 0.2478 in 2000 to 0.6190 in 2022, which is less than that of the industrial subsystem. It can also be observed that before 2014, the orderliness of industry was lower than that of education, indicating that during this period, industry development lagged behind edu- cation development, which restricted the improvement of the integration level between Table 3. Entropy weight of indicators. Subsystems Index C1 C2 C3 C4 C5 C6 C7 Industry subsystems Ej 0.8650 0.9113 0.8891 0.8884 0.8551 0.9235 0.8678 ωj 0.0950 0.0624 0.0780 0.0785 0.1020 0.0538 0.0931 Index C8 C9 C10 C11 C12 C13 — Ej 0.8648 0.8741 0.9379 0.9463 0.8394 0.8648 — ωj 0.0952 0.0886 0.0437 0.0378 0.1130 0.0952 — Subsystems Index J1 J2 J3 J4 J5 J6 J7 Education subsystems Ej 0.8663 0.9330 0.9461 0.9299 0.9298 0.9006 0.9361 ωj 0.1233 0.0618 0.0497 0.0647 0.0648 0.0917 0.0590 Index J8 J9 J10 J11 J12 J13 — Ej 0.8774 0.9010 0.9616 0.9049 0.8828 0.9464 — ωj 0.1131 0.0913 0.0355 0.0877 0.1081 0.0495 — https://doi.org/10.1371/journal.pone.0308572.t003 Table 4. Orderly development level of industry and education subsystem. Year 2000 2001 2002 2003 2004 2005 2006 2007 Industry subsystem 0.2151 0.1388 0.1472 0.1587 0.1386 0.1252 0.1445 0.2040 Education subsystem 0.2478 0.3075 0.2818 0.2674 0.2655 0.2527 0.3092 0.3169 Year 2008 2009 2010 2011 2012 2013 2014 2015

Industry subsystem 0.2644 0.2692 0.3482 0.3654 0.3427 0.3970 0.4478 0.4929 Education subsystem 0.3293 0.3336 0.3642 0.4201 0.5266 0.4259 0.4546 0.4743 Year 2016 2017 2018 2019 2020 2021 2022 — Industry subsystem 0.5431 0.5828 0.6063 0.6616 0.6509 0.7476 0.6928 — Educational subsystem 0.4752 0.5026 0.5264 0.5795 0.6054 0.6105 0.6190 — https://doi.org/10.1371/journal.pone.0308572.t004 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 14 / 22