Research on the Performance Evaluation Model of Higher Education Teachers Based on the Improved Grey Clustering Analysis Method

—Effective performance evaluation of university teachers is supposed to guide teaching behaviors and teaching modes as well as improve teaching quality of higher education. In response to the complexity of performance evaluation of university teachers, this thesis proposes a performance evaluation model based on the improved grey clustering analysis method. Firstly, an index model for evaluating performance of university teachers is established with confirmed layers and index sets. Secondly, performance evaluation grades are given out and whitenization weight functions of grey clustering under different performance grades are established. Based on the standardization of index model, and taking weight into consideration, this thesis provides an improved grey clustering analysis method for performance evaluation of university teachers. Last but not the least, the model is verified through case study to prove its efficacy and availability, which lays a sound support for improving higher education.


INTRODUCTION
Teachers, as a crucial part in higher education, play an important role in advancing teaching modes and the capability of higher education [3][4]. Therefore, the significance of establishing a system and model for evaluating performance of university teachers cannot be overlooked. Experts and scholars have discussed and analyzed such issue from different perspectives and acquired fruitful results [5][6][7][8]. Schools of higher education serve as a cradle for talent training. They are essential in disseminating, imparting and innovating knowledge useful for social and scientific development. Universities, as a result, are faced with the demand of adapting to social and scientific development [1][2].
However, the performance evaluation of university teachers is complicated system engineering. Current study is still far from enough. For example, the existing evaluation system draws much attention on parts rather than a comprehensive analysis; the evaluation target is sometimes mistaken and becomes distant from the purpose of improving education ability; the evaluation process is unclear, failing to deal with fuzzy information or resulting in improper integration of qualitative and quantitative evaluation. Therefore, this paper draws merits from previous studies with the intention of improving education ability, and proposes an improved grey clustering analysis method [11][12][13] for evaluating performance of university teachers, so as to provide guidance and support for improving teaching modes in higher education.

II. PERFORMANCE EVALUATION MODEL OF UNIVERSITY TEACHERS
Under the principle of being scientific, comprehensive, objective, practical and adaptive, this thesis studies carefully the teaching ability, research ability, social service, talent training and ethics and moral development, all of which are primary indexes. Secondary indexes are formed after each primary index is detailed. Table 1 shows the performance evaluation model of university teachers.
III. PERFORMANCE

A. Improved whitenization weight function
The whitenization weight function is a key link of grey clustering analysis. To make sure that the whitenization weight shares the same membership degree with the performance evaluation grade, we have to satisfy the premises that the whitenization weight function is a constant function changing with independent variable and that the whitenization weight functions of every two grades that are no adjacent to each other do not have intersections. And each whitenization weight function has the quantity value of 1 and on each side of the quantity value the function is monotonous. The improved whitenization weight function is constructed in Fig.1.
According to Fig.1, the corresponding whitenization weight function model can be constructed as:

B. Establishing performance evaluation grade
To effectively evaluate the grade of the subject, this thesis adopts a five-grade evaluation mechanism after consulting experts, scholars and leaders in the education sector while abiding by relevant systems and standards.
The five grades are excellent , good , mediocre , general and poor . In order to achieve the same membership scale of evaluation subjects, this thesis adopts a 0-1 grade to divide the performance evaluation interval. The excellent grade is 0.9-1.0, followed by the good grade, which takes up 0.8-0.9. Next is the mediocre grade, taking up 0.7-0.8, followed by the general grade, which takes up 0.6-0.7. And the last is the poor, taking up 0 -0.6. So, the grade set of performance evaluation of university teachers is expressed as: C. Standardization of evaluation index From the evaluation system, it can be seen that performance evaluation grades for different teachers are presented in different forms. Some are qualitative description and others are quantitative description. There are positive indexes, negative indexes and moderate indexes. Thus, we need to standardize these indexes to evaluate based on unified grade.
Qualitative indexes usually have fuzzy qualitative description. The fuzzy language needs to go through quantitative transformation according to grade of qualitative description. The finer the grade, the more definite the quantitative value is after transformation. This thesis adopts 0-1 scale to conduct quantitative transformation on qualitative indexes. 1 refers to excellent qualitative description and 0 refers to poor qualitative description. Other quantitative values are confirmed based on fuzzy description.
For positive quantitative index , if the initial value is , the maximum threshold of its corresponding index is

D. Establishing the performance evaluation model
Based on the grades of performance evaluation of university teachers, we can work out the whitenization weight function of five grades, namely The whitenization weight function The whitenization weight function In the model, with the weight of index k in the sec-  I  I  I  II  II  l  l  kl  q q k w w w The bigger the comprehensive grey clustering coefficient l ! is, the closer the grade of the evaluated teacher to grade l and vice versa. So, comprehensive grey clustering coefficient l ! enables us to figure out in which grade the subject falls.

E. Realization of performance evaluation algorithm
As is discussed above, the performance evaluation model of higher education teachers based on the improved grey clustering analysis method is exercised as below: Step1 Construct the performance evaluation model of university teachers and obtain the primary index set and the secondary index set according to Equ. (1) and (2).
Step 3 Construct the grade of performance evaluation of university teachers according to Equ. (6).
Step 4 Standardize qualitative indexes and quantitative indexes according to Equ. (7)- (9) and description in Section 3.3 to unify the standard.
Step 5 Construct the whitening weight function model of performance evaluation according to Equ.  Step 6 Obtain the comprehensive grey clustering coefficient of subjects under different performance evaluation grades according to Equ. (16)-(17).
Step 7 Obtain the grade of the subject based on the comprehensive grey clustering coefficient.

IV. CASE STUDY AND ANALYSIS
This thesis explains the model and the algorithm with the study of the performance evaluation of teachers in a university. The performance of a teacher is confirmed through the combination of several ways including expert scoring, questionnaire and statistics. These data are standardized as required, and the result of which is shown in Table II , from which we can see the teacher is in the excellent grade.
Thus, construct the whitening weight function model of performance evaluation of teachers and obtain the grey clustering coefficient, as shown in Table III and IV.  To better guide teaching behaviors and teaching modes, and improve the quality of higher education, this thesis proposes a performance evaluation model of university teachers based on the improved grey clustering analysis method. By establishing the index model and improved whitenization weight function, this thesis also standardizes indexes and acquires grades of performance evaluation of teachers. The model is easy to calculate and has a clear physical significance. It provides guidance for improving teaching ability of university teachers.