Group Performance Evaluation in Universities with Entropy Method

DU Xiao-qin (杜小琴) ，MA Hong-qiang (马洪强)，ZHANG Zhao-chun (张兆春)

1 Personnel Department，Donghua University，Shanghai 201620，China

2 Personnel Department，Shanghai Institute of Visual Art，Shanghai 201620，China

Introduction

With the advent of personnel systems reform in universities，it is emergent to find an efficient strategy for group performance evaluation.In practice，a good scientific and impartial method can consistently guide a group in the right direction，rationally allocate human resources，and substantially improve the performance［1］.Therefore，it is important to establish a group performance evaluation scheme with university characteristics that can facilitate the development of colleges and universities，arouse the enthusiasm of team work，and enhance the efficiency of human resource management.All of these have great practical significance.

Group performance evaluation can be modeled as a multiobjective decision-making problem.Recent years have witnessed many methods to study the performance of teachers in university，such as fuzzy comprehensive evaluation (FCE)［2］，analytic hierarchy process (AHP)［3-5］， TOPSIS［6-7］， and principal component analysis(PCA)［8］.The main idea of these methods is based on the computation of the dominant eigenvector first，and then convert the ranking problem into a multi-objective decision-making problem.However，due to the lack of knowledge and data，many attributes of these methods are difficult to identify，and thereby reducing its practicability in real applications.Moreover，existing works mainly focus on individual performance assessment， without the judicious consideration of group performance assessment.Inspired by these，this paper focuses on effective methods for group performance evaluation.Our solution is based on two key factors:first， a continuous ordered weighted operator is introduced， aiming at eliminating uncertainty evaluation information;then，a novel entropy method is proposed to provide theoretical guarantees for group performance evaluation.

1 Research Methods

When a group evaluation index system is designed，it is necessary to consider the function of universities and colleges，its running characteristics，and the long-term practicability.There are three noteworthy factors:(1)the perspectives of which a group is evaluated［9］，(2)the evaluation index，and(3)the index weights.Since different evaluation index has a huge impact on group performance，is distinct，the index weight often varies with different evaluation index.Hotelling used the relevant variables to replace irrelevant variables as a linear combination of form［10］，so we determine the group of the performance evaluation model:

where ωiis the i-th weight，xiis the i-th evaluation value，and y is the entire evaluation value.

(1)Selection of college group assessment evaluation index

Colleges and scientific research units are usually the objects of group assessment in this research.Colleges undertake the tasks，including teaching and scientific research，personnel training，and teaching staff construction.

(2)Personnel training work

The number and the level distribution of academician of Chinese academy of sciences， chief scientists， national outstanding youth，the Yangtze river scholars，the inclusion of one-thousand talents，and the funding schemes for excellent young university teachers of the ministry of education are the important indicators of group training.

(3)Scientific research work

The quality and quantity of academic papers are the important indicators of group performance.To follow the new trend of scientific development and own a field of itself，a college has to follow the dynamic discipline frontier and get new breakthroughs in the field.First of all，a college should follow the steps of the journals with the highest impact factor and try to get its latest scientific achievements published on the journals.In this way，a college can always understand and lead to the right direction;the more project funding，the more opportunity to get more support of innovation and higher honor award.

(4)Discipline construction work

Subject development is the core of knowledge discovery and innovation.The number of key disciplines，Dr Points，the scientific research achievements，and high level papers are important in discipline construction.Whether college attaches great importance to the breakthrough of subject development，efforts to improve the level of discipline is important to measure college development.

(5)Construction of teaching team

A good teaching team must be built in a reasonable way.The national government encourages to enhance the study and academic level of teachers' development.Teacher's development center has been established in many universities.College can actively use a variety of opportunities to create conditions and structure platforms for young teachers.Also，the backbone teachers should play the role of demonstration.To build a team with reasonable knowledge structure and age structure，title structure is one of the evaluation indices of college leadership.

(6)System construction and operation

Nothing can be accomplished without laws.Whether a group of systems is operated in the right way is the essential condition about the rise and fall of the team.According to the new thoughts and new questions，the principle of democracy，fairness，and impartiality should be insisted on and should be under the supervision of the public.Then this system construction can reflect public opinion，and is the source of the collective cohesion.

The above analysis suggests the five indexes that constitutes a group of colleges and universities evaluation index system.

2 Group Performance Evaluation Method with Entropy Method

Groups of colleges and universities evaluation is a process of participating，the interval number should be chosen to represent the group performance evaluation result［11］.That is，after dealing with the result of expert scoring，we take the concentrated interval as the evaluation results.Due to the hardness to compute an interval，it is necessary to eliminate uncertainty evaluation information.

2.1 The selection of evaluation index and the way to eliminate uncertainty evaluation information

The results of evaluation can be characterized as interval numbers，but it is hard to obtain the accurate interval numbers.To eliminate uncertainty evaluation information，we apply the following methods［12］:

where ρ(y)is a monotonic function of the basic unit interval，and generally，ρ()y = yry ≥()0

Using Eq.(2)，we can readily map an interval into a value，and achieve the purpose of the quantitative.Obviously，it will reflect the group's performance and quality of work more accurately［13］.

2.2 Decision matrix and index normalization

By the above analysis we can get a multi-object decision matrix［14］

2.3 The calculation of entropy

After the row normalization，we substitute the matrix X'into the entropy formula［12］:

which produces the entropy value of the index:

It can be discerned that the coefficient of variance 1 - Eidecreases with the growing information entropy.Thus，to ascertain the weight of evaluation indexes，we expect that the greater the value difference，the greater the indicators.Hence，it is reasonable to weigh the index by 1 -Ei［15］.

2.4 The weight of entropy

The weight of entropy，denoted as ωi，is defined to be

The index weight obtained by the formula，corresponds to the five indexes of weight vector obtained by the entropy weight method:

3 The Example Analysis

The annual performance of a college or a scientific research unit is evaluated by universities.Each group should set a new goal for new year work on the basis of summarizing the work achievement this year.At the same time，certain reference should be suggested by them and it benefits the further management，especially teachers' salary adjustments.Let's take an university as an example.It sets up evaluation index from personnel training，scientific research，discipline construction，the construction of teachers' team，the system construction and operation and thus，we get the data in the following tables:

Table 1 Experts Score

According to Eq.(2)，with continuous ordered weighted operator ρ()y = y3to eliminate uncertainty evaluation information，we get the following matrix as shown in Table 2.

To normalize the evaluation matrix in each column by Eqs.(3)and (4)，we get the following judgment matrix as shown in Table 3.

Table 2 Canonical matrix

Table 3 Normalized matrix

With entropy method by formula (1)，we obtain the five weight vectors from the normalized evaluation matrix.

To calculate the scale of the group performance appraisal value.

The value is:

According to the analysis of score matrix，group G gains outstanding achievements in all aspects.On the other hand，group F is weaker due to the weak construction of teachers team and needed laws.An analysis of the evaluation experience and more powerful ways to strengthen the teaching staff's academic capabilities altogether pave the way for F to gain high score in this evaluation system.

4 Conclusions

This paper proposed a systematic approach to group performance evaluation.First，a continuous ordered weighted operator was introduced to eliminate uncertainty evaluation information.Then，a entropy-based method was proposed for group performance evaluation.The integration of these two methods allows us to assess group performance more scientifically，and with high quality.

Actually，the results based on the data of one university's yearly evaluation，so it is to some extent sample-directed.Due to the study of the performance appraisal in our country is relatively lagging behind，the construction of evaluation index system for colleges and universities lacks scientific norms and standards.To the best of our knowledge，there is barely special document formulated so far.The variability and complexity of the group assessment of colleges and universities have a huge influence on the establishment of objective evaluation standard.As a future avenue，we are experimenting with a more systematic method that can further enhance the semantics and flexibility of the proposed method for group performance evaluation.

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