A New Fuzzy Comprehensive Evaluation Model for Influencing Factors of Physical Education

— Education evaluation promotes the scientific management of physical education (PE), and facilitates the realization of teaching goals of PE lessons. Through fuzzy comprehensive evaluation (FCE), this paper explores the influencing factors of teaching evaluation system for PE. A new evaluation index system (EIS) of PE was constructed through expert evaluation, the weight values of each index were determined through analytic hierarchy process (AHP), and an FCE model was established for PE. Taking a college PE teacher as the research object, the application effect of the proposed FCE model was empirically investigated. The results demonstrate the practicality and feasibility of the proposed model. The FCE model can qualify PE evaluation results com-prehensively, and support the overall evaluation of a single factor. The model-ing results reflect the actual teaching effect from multiple layers, and help to ra-tionalize PE in the light of specific factors. The research provides important theoretical and realistic evidence to the promotion of PE evaluation.


Introduction
As education reform is being promoted and deepened constantly in China in recent years, the teaching philosophy, teaching modes, and teaching methods of PE have been reformed in an all-round way. To test whether these reforms are scientific, reasonable, and effective, corresponding evaluation means are required, and the education evaluation is of crucial importance to the management, decision-making, development, and reform of education. Now, education evaluation has become an important part of education works, therefore, establishing suitable PE evaluation systems are of great necessity.
Studies have shown that education evaluation originated in China [1]. Ever since China has determined the education goals of developing quality education, focusing on students' physical quality growth, and cultivating students to have a life-long habit of physical exercise, domestic education scholars have gradually turned their eyes on the research of PE evaluation, and many of them have conducted related research from different perspectives and achieved fruitful results. For example, some explored the theories, methods, and status quo of PE evaluation [2]; some analyzed the influencing factors of PE evaluation [3]; some constructed various EISs for PE evaluation, and employed real cases to perform empirical research [4]. However, currently, there isn't a uniform standard for PE evaluation in China, and the existing PE generally emphasizes too much on the lecturing of PE knowledge and skills, while ignoring the evaluation on the students' physical quality, ability, and interest, moreover, the evaluation subjects are not as varied [5]. Foreign research's PE evaluation is more systematic and comprehensive, and can reflect PE students' learning attitude, ability, interest, and individual development [6]. For example, the United States have adopted an alternative PE evaluation method which lays stress on students' ability in applying PE knowledge and skills in practice [7]; the Japanese respects individual differences during PE evaluation, they formulated personalized evaluation criteria to trigger students' PE learning enthusiasm [8].
After carefully reviewing and analyzing relevant literatures, this paper established a new EIS for PE evaluation, and constructed a PE evaluation model based on FCE; then, the proposed model was subject to empirical study to verify their feasibility and practicality.

About the new EIS
Besides research papers, we also analyzed relevant documents issued by the Chinese government, and determined a few evaluation indexes from four aspects of teaching preparation, teaching process, teaching effect, and teaching evaluation according to four evaluation principles of scientificity, comprehensiveness, objectivity, and feasibility [9]. After consulting opinions of experts and teachers, at first, an EIS with 4 first-level indexes, 11 second-level indexes, and 30 third-level indexes was established initially. Then, experts were invited to screen the indexes and determine their importance, and 2 third-level indexes had been deleted per their opinions; finally, an EIS with 4 first-level indexes, 11 second-level indexes, and 28 third-level indexes was established, as shown in Table 1 [10].

3
About the FCE-based PE evaluation model

Determination of index weight values
This paper used AHP to determine the weight values of indexes at each level. First, the EIS was constructed, and the hierarchical relationships among the indexes were analyzed. Then, 15 experts and teachers who are familiar with the teaching evaluation of the PE major were invited to use 1-5 scales to compare the indexes in pairs and construct the corresponding judgement matrix, as shown in Table 2 [11]. After that, the judgement matrix was calculated, normalized, and subject to consistency test. If the matrix passes the consistency test, it means that the calculated weight coefficients are reasonable, and it can reflect the relative importance of each index in the EIS; if the matrix fails to pass the consistency test, it needs to be re-adjusted until it could pass the consistency test [12]. The former is slightly more important than the latter 5 The former is more important than the latter 7 The former is obviously more important than the latter 9 The former is absolutely more important than the latter 2, 4, 6, 8, 10 Importance lies between two adjacent levels 1, 1/2, 1/3, …, 1/9 The latter takes the reciprocal of the importance of the former With the second-level index "teaching file" under the first-level index "teaching preparation" as an example, an expert judgement matrix was constructed: According to Formula (1)-(3), after calculation, it's obtained λmax=4.741, CR=0.082<0.1, which mean that the judgement matrix is consistent, and the assigned weight values could reflect the importance degree of each index [13]. Using the same method, the weight values of other indexes could be obtained as well, the details are listed in Table 1. (1) RI is the random index, and its value could be obtained by looking up the table; according to the condition in this study, when n=4, RI value is 0.9 [14].

3.2
Construction of the FCE-based PE evaluation model

Construction of the evaluation factor sets
Based on above-established EIS for PE evaluation, the evaluation set of first-level indexes could be obtained as: The evaluation sets of second-level indexes could be obtained as:   ,, The evaluation sets of third-level indexes could be obtained as:

Construction of the weight value sets
Through the AHP mentioned in above paragraphs, the weight values of indexes at each level could be obtained: Its corresponding value set is: Table 3 lists the scores corresponding to the value set [15].  5. The quantified score of the comprehensive evaluation is:

A empirical study on the proposed model
To verify the practicality and feasibility of the proposed EIS and model, a PE teacher A was selected as an evaluation object, and 10 supervisors were invited to attend the class taught by teacher A and give evaluations on the teacher using the proposed EIS, the evaluation results are shown in Table 4, the values in the table represent the number of supervisors who had chosen the corresponding option. Therefore, the FCE matrix of teaching evaluation is: The FCE set of teaching evaluation is: According to the quantified evaluation results, the comprehensive score of teacher A was 90.3615, which was between 90 and 100, and the evaluation grade was excellent. In order to better understand the strengths and weaknesses of this teacher, the model can also give FCE on each single index of the teacher.