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

For positive indexes (the larger the superior), the formula above is suitable. For the reverse index (the smaller the superior), the following formula is suitable. The processing result forms the standardization matrix R = (rij)m×n, 0 � rij � 1. For an index, the greater the difference in the evaluation index values, the larger the amount of information contained in this index, and the greater the effect of this index. According to the concept of entropy, the increase in information means a reduction in entropy, and entropy can be used to measure the size of this information. The feature proportion of year i under index j can be defined as follows: pij ¼ rij X m i¼1 rij ð7Þ The Shannon entropy of index j can be defined as follows: Ej ¼ kX m i¼1 pij ln pij j ¼ 1; 2; 3 . . .n ð8Þ In the formula, k = 1/ln m, when pij = 0 and pij ln pij = 0. The entropy weight of index j can be defined as follows: oj ¼ 1 Ej n X n j¼1 Ej ð9Þ In the formula, 0 � ωj � 1, X n j¼1 oj ¼ 1, and the characteristics of the entropy weight are as follows: When the index values of each evaluated object are entirely equal, the entropy value is the maximum, and the entropy weight is zero. This means that the index does not provide any use- ful information for decision-makers; this index can be considered canceled. When the index values of each evaluated object are quite different, the entropy value is smaller, and the entropy weight is large. This means that the index provides decision-makers with useful information, and this index should be focused on.

The larger the entropy value of the index is, the smaller the value of entropy weight, and the less important the index. Entropy weight has special significance; it is not the actual importance factor of the given indexes in the process of decision or assessment but rather the relative intensity factor of each index in a competitive sense under the condition that each evaluation index value has been determined after a given set of evaluated objects. From the information point of view, entropy weight represents the extent of useful informa- tion provided by the index in question [54]. 3. Empirical research and results analysis 3.1 Research process Firstly, empirical research is conducted based on the statistical data of Chongqing from 2000 to 2022, which are sourced from the "Chongqing Statistical Yearbook" from 2001 to 2023. The original statistical data of the "higher education gross enrollment rate" from 2000 to 2006 are missing, and linear interpolation is used to fill the gap. 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 12 / 22