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

For a particular assessment problem, there is a raw data matrix X formed of m years and n indexes; the element xij in the matrix represents the raw data value of the year i(i = 1,2,. . .,m) to the index j(j = 1,2,. . .,n). X ¼ x11 x12 . . . x1n x21 x22 . . . x2n . . . . . . . . . . . . xm1 xm2 . . . xmn 2 6 6 6 6 4 3 7 7 7 7 5 ð5Þ The raw data in matrix X must be standardized to eliminate the effects of different dimen- sions and magnitude, and then, these data can be used in entropy calculations. Standardization operation should utilize an appropriate calculation method in accordance with the entropy cal- culation and the nature of the indexes. Commonly used standardization methods, such as z- score and equalization, could eliminate the effects of different dimensions and magnitudes [51]. Therefore, the z-score method is not suitable for use because the data normalized by this method are distributed between -1 and 1, and there is a logarithm in the entropy calculations. The equalization method could not guarantee that the value of all processed data is positive, and thus, it is also not suitable for use. Range standardization is a suitable method here [52, 53], and its formula is as follows: rij ¼ xij minðxijÞ maxðxijÞ minðxijÞ ; for positive indexes rij ¼ maxðxijÞ xij maxðxijÞ minðxijÞ ; for reverse indexes 8 > > > > < > > > > : ð6Þ Table 2. Higher education subsystem indicators. Frame Dimension Index Statistical calculations Structure Education structure Percentage of education funds (j1) Education funding/GDP × 100% College student teacher ratio (j2)

Number of students in ordinary colleges and universities/number of teachers in ordinary colleges and universities Conduct Education scale School size (j3) The number of ordinary higher education schools Student scale (j4) Number of students in regular institutions of higher learning Education develop Per capita education funding (j5) Educational funding/number of students in regular higher education institutions Educational infrastructure (j6) The number of public libraries in the area Increase in faculty strength (j7) (Number of teachers in the current period—number of teachers in the previous period) / number of teachers in the previous period × 100% Educational funding increase (j8) (Current education funds—previous education funds) / previous education funds × 100% Growth in school scale (j9) (Number of students in the current period—number of students in the previous period) / number of students in the previous period × 100% Performance Education input Capital investment (j10) Expenditure on education in local fiscal budget Teaching staff input (j11) Number of full-time teachers in regular higher education Education output Level of higher education (j12) The number of students in higher education institutions per 100,000 population Higher education opportunities (j13) Gross enrollment rate of higher education https://doi.org/10.1371/journal.pone.0308572.t002 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 11 / 22