Fuzzy comprehensive evaluation of physical education based on high dimensional data mining

Abstract

The spectrum cluster algorithm is opposite in the other cluster algorithm has the obvious superiority that can distinguish the non-raised distribution the cluster, suits extremely in many actual problems. With this prior model this paper combines the fuzzy set system to propose the new data mining algorithm. At the same time, we build a fuzzy comprehensive evaluation model and analyze the evaluation system of physical education. The result shows that the fuzzy comprehensive evaluation method is improved by using the grey relational grade, which avoids the disadvantages of adopting the principle of maximum membership degree. Therefore, this evaluation method can be used in the evaluation of public sports teaching in colleges and universities.

Keywords

Mining algorithm grey system public physical education high dimensional data fuzzy comprehensive evaluation

1 Introduction

Nowadays, the information technology in our country is developing rapidly, and information technology is changing our lives. With the development of globalization, great changes have taken place in China’s higher education. Under the current educational background, school physical education is one of the members of the campus education in our country, which plays an important role in the development of school teaching [1]. As the end point of campus education in China, university education is the last stop before students enter the society. Therefore, the university education must control the quality, so as to lay a solid foundation for these social systems that are going to enter the society [2, 3]. Public physical education is a course for students of non-physical education major in Colleges and Universities [4]. Its purpose is to let students continue physical exercise, master certain sports skills, cultivate body building consciousness, and improve physical quality. In order to better adapt to the social environment in the future, it is necessary to be more rigorous in teachingevaluation.

For the teaching management work, classroom teaching quality evaluation is one of the important content. Scientific and reasonable evaluation of classroom teaching quality can greatly promote the improvement of teaching quality [5, 6]. However, in order to make classroom teaching quality evaluation play a proper role in promoting it, we must use rigorous rating methods, and ensure the reliability and accuracy of the evaluation results. The ideal reliability and validity of the evaluation results need scientific, normative and feasible evaluation methods as guarantee. In the past, the classroom teaching quality evaluation method of public sports is fuzzy. Based on the theory of fuzzy comprehensive evaluation, this paper constructs an evaluation index system with expert opinion as the evaluation subject, and applies AHP and grey system theory to the comprehensive evaluation of classroom teaching. As far as possible, the author can make teaching quality evaluation more accurate, objective, and practical.

2 The proposed model

In order to solve the multi-dimensional data model and between the relations data model bidirectional data system inquiry, questions and so on data clean, data conversion, this research through to the concept standard correlation research, unified the global data excavation and the partial data mining [7], and we proposed one kind based on the partial information overall situation concept standard data mining algorithm improvement, the realization centralism, the distribution data accuracy and the uniformity[8, 9]. With the development of fuzzy mathematics and neural network, the fuzzy neural network has been successfully applied in the fields of expert system, control system, pattern recognition and system modeling [10, 11].

2.1 The high dimensional data features

In multi-dimensional data parallel I/O is divides the multi-dimensional data certain sub-block data will be in the identical sub-block data the data object to save in together and all sub-block data distribution will save time on the floppy disk [12]. When carries on the data accessing, only needs by the parallel I/O way visit certain quantity floppy disk and the correlation sub-block data that can obtain the data object which needs, when like this carries on the visit, both can realize the parallel processing, and that can reduce the I/O execution the total data quantity, as thus enormously reduces the total time delay which creates by the I/O operation enhanced the data accessing and the parallel I/O efficiency [13].

To propose the targeted solution to the high dimensional model, we refer to the Fig. 2, the spatial filling curve is a method of the mapping d-dimensional space into one-dimensional space. It passes through each discrete element in a high-dimensional space like a line, and traverses only once. It numbers the cells in a linear order which have the basis of the following formulas and equations.

Fig. 2.

The Transferred Target High Dimensional Data Model.

$M_{k} \overset{def}{=} \underset{m \in \bar{1, M_{k}}}{max •} {α_{k, m} H_{k, m}} \in R^{N \times N}$ (1)

$\begin{matrix} M_{k} [i, j] \geq (M_{k} \circ M_{k}) [i, j] \\ = \max_{n \in \bar{1, N}} {M_{k} [i, n], M_{k} [n, j]} \end{matrix}$ (2)

$\begin{matrix} S_{μ} (R_{k}) = - \sum_{i = 1}^{N} \sum_{j = 1}^{N} M_{k} [i, j] \log_{2} M_{k} [i, j] \\ - \sum_{i = 1}^{N} \sum_{j = 1}^{N} [1 - M_{k} [i, j]] \log_{2} [1 - M_{k} [i, j]] \end{matrix}$ (3)

Where the $\underset{m \in \bar{1, M_{k}}}{max •} {α_{k, m} H_{k, m}}$ represents the objective function, the multidimensional spatial data minimum spanning tree normality test method based on the test data and generated by the Monte Carlo method and has the same capacity as the mean and variance, mixed multivariate normal data, calculation of mixed data concentrated all samples of the Euclidean distance between, the $max_{n \in \bar{1, N}} min {M_{k} [i, n], M_{k} [n, j]}$ represents revised form of the target model and the S_μ (R_k) is the optimized expression of the model to the analyzed[14, 15]. After has used the position processing strategy, for enhances the efficiency that uses the static two-dimensional array K when preserved structure U joins the element takes in U the data redundant data, because which positions searches in the binary position string for really is consumes relatively the time. Simultaneously the position processing strategy causes the V each point length size to be equal, the target function is transferred into formula 4. $∥ \nabla S_{μ} (R_{k}) ∥ = \sqrt{\sum_{i = 1}^{N} \sum_{j = 1}^{N} {[\log_{2} \frac{1 - M_{k} [i, j]}{M_{k} [i, j]}]}^{2}}$ (4)

Where the ∥∇ S_μ (R_k) ∥ denotes the revised form of the model, and the $\frac{1 - M_{k} [i, j]}{M_{k} [i, j]}$ is the revised form of the data judgement term. To solve the formula 4, we should the follow the listed restriction conditions. $μ (x) = {\begin{matrix} 1, \\ 1 - (m - x) / Δ, \\ 1 - (x - m) / Δ, \\ 0, \end{matrix} \begin{matrix} x = m, \\ m - Δ < x < m, \\ m < x < m + Δ, \\ elsewhere . \end{matrix}$ (5) $μ_{P_{d} (t)} (x) = {\begin{matrix} 1, \\ 1 - (P_{d} (t) - x) / Δ_{d} (t), \\ 1 - (x - P_{d} (t)) / Δ_{d} (t), \\ 0, \end{matrix} \begin{matrix} x = P_{d} (t), \\ P_{d} (t) - Δ_{d} (t) < x < P_{d} (t), \\ P_{d} (t) < x < P_{d} (t) + Δ_{d} (t), \\ elsewhere, \end{matrix}$ (6)

SFBS is smaller than I/O when the characteristic dimension, the obtained result good in SFFS, the characteristic dimension big child 110 o’clock situations is opposite. SFFS is in each time found one from the surplus characteristic to choose the characteristic subset most meaningful characteristic regarding oneself, and joins to this characteristic subset, then the basis controlled condition, in the dynamic rejection selection characteristic subset most does not have the significance the characteristic, while finally obtained is the final characteristic subset [16, 17]. The model is transferred into Fig. 2.

T distribution data is selected for the basic non-normal distribution data because the T distribution data is significantly different from the normal distribution data when the degree of the freedom m is relatively small and gradually becomes close to the normal distribution data when m is gradually increased, Gradually close to the normal distribution of the data can be compared to the two test methods test “abandon pseudo” ability [18, 19]. The modified K-Nearest Neighbor algorithm divides the verification process into three correlation stages: the correlation phase, the inspection period and the retention period. Since the typical spatiotemporal information fusion scheme has the property of being able to correlate the present test with the historical test as the follows.

$\begin{matrix} z^{*} = \max μ_{D} = \max \min (μ_{J}, μ_{P_{d} (1)}, …, μ_{P_{d} (T)}, \\ μ_{P_{r} (1)}, …, μ_{P_{r} (T)}) \end{matrix}$ (7)

$\begin{matrix} \min_{0 \leq z \leq 1, p_{t i} (t), p_{b m} (t)} b {(z - 2)}^{2} \\ + J + λ_{J} (z Δ_{J} - J_{o} - Δ_{J} + J) \end{matrix}$ (8)

From the above results, we can see that if the m-dimensional components of the Y are normal distribution, we can know that Y obeys the normal distribution, and prove that the original data X also obeys the normal distribution. So the problem of multidimensional normality test is turned into one-dimensional normality test.

Fig. 4.

The Visualized Uncertainty Criteria.

2.2 The uncertainty criteria

Set pair analysis is a systematic analysis method to deal with the uncertainty problem. Its core idea is to analyze and deal with the deterministic relation and uncertainty relation between the objective things being studied as an uncertainty system. The set pair is a pair consisting of two sets with definite relation. The set principle is the identity, difference and opposition of the two sets (A, B) of the set pair under certain background analysis.

In the above Fig. 3, we show the forms of the uncertainty criteria, the so-called not deterministic AHP, mainly is refers in the decision-making process, the people when the different plan carries on the comparison to the identical criterion under that is unable with a definite value to express the comparison result. Indefinite the AHP and the deterministic AHP computational method are on the whole similar, but also have its special algorithm that displays especially in the judgment matrix structure method. The traditional method is to judges the matrix element the probability distribution to make the hypothesis. With this concern, we define the systematic model as theformula 9.

Fig. 3.

The Forms of the Uncertainty Criteria.

$\begin{matrix} P (F_{p}, F_{q}) = \sum_{μ} f (μ : F_{p}, F_{q}) \\ = \sum_{μ} \sum_{j = 1}^{n} δ (x_{j}, μ : F_{p}, F_{q}) ω (x_{j}) \end{matrix}$ (9)

Where the δ (x_j, μ : F_p, F_q) ω (x_j) represents the specific problem, its basic core is to determine the coefficient of uncertainty i and we determine that basic degree of the connection of the specific problem is also determined. Reasonable determination of i is the focus of this paper [20, 21]. Considered in indefinite the AHP the weight indicated by the sector number, therefore between them is different between the general determination value the comparison, while but is between the sector number comparison and because waits the comparison sector to count A and B expresses a some plan relative criterion important degree scope, therefore regarding the relative important comparison results which expressed by the basic sector number may be similarly the important degree compares relatively, therefore should not determine likely the value such indicated by the two business, but may use the two important difference the logic operation expression that can be visualized as the follows.

According to the approximate range and approximation theory, the larger the range, the greater the uncertainty; Range is smaller, the greater the uncertainty. Thus the algorithm according to the size of weighting interval width is considered in the sorting: width as the accurate sorting which should follow the listed procedures and steps. $H_{kl} = - E_{kl} {log}_{2} (E_{kl}) - (1 - E_{kl}) {log}_{2} (1 - E_{kl})$ (10)

$\begin{matrix} H_{k} = \sum_{l = 1, l \neq k}^{n} [E_{k l} \\ \log_{2} (E_{k l}) - (1 - E_{k l}) \log_{2} (1 - E_{k l})] \end{matrix}$ (11)

Where the (1 - E_kl) log ₂ (1 - E_kl) and the E_kl log ₂ (E_kl) are the revised terms, by using the upper and lower bounds calculation models of Sugihara, Maeda and Tanaka, the weight interval of each scheme relative to a certain criterion is calculated as shown in the equation 12, where the S (F_p, F_q) is the revised target function. $S e p (c, U) = 1 - \underset{p \neq q}{\min_{︸}} S (F_{p}, F_{q})$ (12)

2.3 The fuzzy mathematics and clustering model

In the mathematical logic development course and the classical mathematical logic is famous by its formalized inference rigorous that is the modern computer science rationale. But in the processing real world massive uncertainty thing aspect which has its limitation actually [22, 23]. Fuzzy mathematics is developing rapidly in both theoretical and the applied fields. The theoretical research is mainly the fuzzification of the classical mathematical concepts. As a result of the hierarchical structure of the fuzzy set itself, this kind of theoretical research is more complicated and more complicated with the attraction [24]. Obviously, regarding the clear thing, whether we can determine the individual to have the subordination relations accurately to the kind, and that deduces side through the precise definition to carry on the qualitative quota strictly the analysis research, how but only can analyze the individual to the fuzzy matter laws of nature to the kind of subordination degree, the utilization fuzzy definition and the likelihood inferential reasoning method carries on the nature and the quantity analysis research to it. It is not difficult otherwise to leave, as the precise method and the fuzzy method have its different research respectively and the applicable scope and they cannot confuse or the substitution mutually [25, 26]. In the table two, we show the current research condition of the fuzzysystem all over the world.

Here, we focus on the theoretical basis of the fuzzy system, in current based on in description logic semantic modelling domain and the researcher cared about the core question is based on description logic semantic model expression ability and the inference order of complexity [27]. As a result of the software system complexity, the researcher favors in uses some complex description logic to express software own series, but complex describes the model inference price which logic brings also unceasingly to enhance, thus restricts the complex description logic in the software modelling application. In formula 13, we define the weight features of the fuzzy system. $w_{m i} = {\begin{matrix} \frac{\begin{matrix} 1 \\ 0 \\ 1 \end{matrix}}{\sum_{s = 1}^{c} [\frac{d_{\log} (z_{m}, x_{i})}{d_{\log} (z_{s}, x_{i})}]} & \begin{matrix} i f x_{i} = z_{m} \\ i f x_{i} = z_{s} b u t s \neq m \\ i f x_{i} \neq z_{m} a n d x_{i} \neq z_{s}, 1 \leq s \leq c \end{matrix} \end{matrix}$ (13)

The basic core of fuzzy logic is the fuzzification of the true concept itself and in our practical thinking activities, we often do not need and in many cases cannot use a precise numerical representation of the true degree of the proposition. Under this basis, we use the fitness function for describing the relationship. $μ_{i j} = \frac{1}{\sum_{l = 1, l \neq j}^{c} {(\frac{D (z_{j}, z_{i})}{D (z_{j}, z_{l})})}^{1 / (m - 1)}} (i \neq j)$ (14)

Where the ${(\frac{D (z_{j}, z_{i})}{D (z_{j}, z_{l})})}^{1 / - (m - 1)}$ represents the objective term, the syntax of numerical fuzzy preferred logic is built on the basis of propositional logic grammar and its extension. Propositional logic language consists of basic atomic variable set and connector set, the formula consists of atomic variable set and the connector set according to certain rules. It is an NP-type likelihood reasoning. The premise and premise of its hypotheses, the posteriori and the conclusion of the hypothesis are only approximate and the fuzzy value of the different language proposition, and it is affirmed by approximating the premise of the large and approximate affirmative Conclusion, so the premise and conclusion between the reasoning only; there is an approximation rather than the logical connection, it is a natural logical reasoning. Therefore, we show the analysis pattern in the Fig. 5.

Fig. 5.

The Fuzzy Reasoning and Analysis Matrix.

2.4 The proposed novel clustering algorithm

The CluStream framework is adopted in most data stream clustering algorithms. This framework is a major breakthrough in data stream clustering research, so this paper chooses CluStream algorithm as the comparison algorithm while although the CluStream algorithm effectively solves the problem of data flow dynamic change [28], because of the clustering using K-means algorithm, so inevitably inherent defects in the algorithm into the CluStream algorithm. The spectrum cluster algorithm is opposite in the other cluster algorithm has the obvious superiority that can distinguish the non-raised distribution the cluster, suits extremely in many actual problems, moreover carries out quite easily. It is one kind based on two similar relational algorithms, first acts according to the data set which assigns to define the description pair data point similarity the similar matrixs and computing matrix characteristic value and characteristic vector, then choice appropriate characteristic vector cluster different data point, the evaluation system of teaching quality as shown in Fig. 6.

Fig. 6.

Evaluation system of teaching quality.

The algorithm considered in the clustering process, influence of the same class in the sample for the cluster center is not the same, for each sample, the sample does not contain a weight class also has inhibition effect, so the membership matrix of each sample weight and the design of improved FCM fuzzy C clustering the adaptive weights in each iteration according to the current state of the data partition, dynamic calculation of sample weights as follows. ${distortion}_{φ} = \frac{1}{N} \sum_{x} {| x - φ (x) |}^{2}$ (15)

$\begin{matrix} d i s t o r t i o n_{φ} \\ = \frac{1}{N} (\sum_{x} | x |^{2} - 2 φ^{T} (x) \sum_{x} x + N | φ (x) |^{2}) \end{matrix}$ (16)

When the data of large data set changes and the incremental clustering algorithm only updates the clustering results incrementally to the changed partial data, and makes full use of the former clustering results to improve the efficiency which is shown as ∑_x|x - φ (x) |², to optimize the traditional model, the 2φ^T (x) ∑_xx is considered and implemented for the later discussions. In the concrete realization process, the different algorithm exists differently in the data set matrix expression. Spectrum cluster algorithm CSC which limits through the direct revision matrix method is paired in the limit information introduction spectrum cluster algorithm, weighted membership matrix such that the farther from the cluster center distance of each sample is the smaller the membership degree belonging to the cluster center as the follows. $\begin{matrix} δ (x_{j}, μ : F_{p}, F_{q}) \\ = {\begin{matrix} ω (x_{j}) & if (μ_{F_{p}} (x_{j}) \geq μ) and (μ_{F_{q}} (x_{j}) \geq μ) \\ 0 & otherwise \end{matrix} \end{matrix}$ (17)

In FCM algorithm, due to the random initial cluster centers, leading to the clustering results of excessive dependence on the initial clustering center in the presence of outlier and the imbalance of the sample distribution, clustering fall into local optimal state. $s = \sum_{i = 1}^{c} \sum_{j = 1, j \neq i}^{c} {(μ_{i j})}^{m} D (v_{i}, v_{j}) (j \neq i)$ (18)

To deal with the challenge, the formula 18 is applied, the (μ_ij) ^mD (v_i, v_j) represents the revised kernel, the connection function value size replaces in the traditional cluster the distance and the similarity factor, and by this measure cluster object between proximity and similar degree. When the algorithm starts, the use initial micro bunch of algorithm carries on the cluster the initialization, then the initial micro bunch of the algorithm will serve as online renews micro bunch of as well as the off-line great cluster foundation algorithm.

3 Evaluation index system

3.1 The establishment of teaching quality evaluation index system

The most effective way to judge the teaching process and the value of achievement is to evaluate the teaching quality [29]. Through the evaluation results, we can learn the quality of teaching, and makecorrect corrections on this basis. Before setting out the teaching quality evaluation, a reasonable teaching evaluation index system must be developed, and the system should be formulated in accordance with the following principles: (1) The relevant characteristics of efficient teaching should be embodied in the index system, so as to give the corresponding practical significance of evaluation tools. (2) Comply with the principle of systematicness. Teaching evaluation should reflect the teaching information of each other, and after analyzing the results of teaching evaluation, it is fed back to the relevant personnel. Only in this way can the evaluation object be evaluated systematically, so as to systematically evaluate the various aspects of the educational object, and provide guidance for the optimization of teaching, and promote the improvement of the teaching level in Colleges and universities. (3) Conform to the principle of science. Regardless of the index or weight, it has the corresponding dynamic attributes, which can reflect the focus of teaching in different stages, and the policy direction of the education sector. It is necessary to ensure that all indicators maintain independent relationships, and the content similarity of each index is not high, and there is no overlap. We should reasonably combine quantitative indicators and qualitative indicators, so as to maintain a high fault tolerance, to ensure that the participants’ subjective factors will not affect the qualitative indicators. In the design of indicators, we should let the evaluation object as far as possible to participate in, only the indicators are widely recognized, so that the evaluation results will be more accurate and reliable.

In this paper, the evaluation index is formulated based on Sports Science, pedagogy, psychology and other disciplines of knowledge, by means of questionnaire (a total of 100 questionnaires, 98 questionnaires were returned), expert forum (10 experts) and logical analysis construction. The idea of weighting the evaluation indicators in this study: The expert questionnaire was given for the first weight assignment. Then the questionnaire was recovered, the statistical results were calculated, and the weighted average value of each index was calculated. The second questionnaire was given second weights assignment, the questionnaire was recovered, the statistical results were calculated, and the weight mean value of each index was calculated. Consistency test was used to establish the weight value. In the past evaluation system, there are often many targets and multiple criterions. If you only use qualitative analysis and logical judgment, it will be difficult to obtainaccurate analysis results. This paper can effectively solve this problem. The detailed evaluation index system is detailed as shown in Table 1.

Table 1
Comprehensive evaluation index system

Primary indices Two level index Index connotation Weight

Teaching preparation 0.1630 Preparation before class The layout of field equipment is reasonable; the task of teaching plan meets the requirements of the plan 0.1289

Task of teaching plan The teaching task is clear, specific and comprehensive, and the teaching content meets the requirements of the task 0.4970

Teaching plan content The arrangement of teaching contents is reasonable and pertinent 0.1813

Key points of teaching plan The teaching content embodies the key and difficult points, and the load arrangement is reasonable 0.1928

Teaching organization 0.3371 Teaching method Proper use of multimedia teaching means 0.2580

Organizational process The arrangement of teaching process is full of rhythm 0.3103

Guidance technology The explanation is concise, the demonstration is right, the instruction technique is just right 0.1355

Teaching emphasis The teaching emphasis and difficulty are prominent, and the purpose is strong 0.2962

Sports load 0.1887 Load content The content of the load is purposeful, targeted, and selective 0.2523

Load density Conforms to the type of class and the characteristics of teaching materials 0.1725

Load intensity The amount, intensity and proper of the class exercise coincide with the teaching content 0.2216

Load adjustment Flexibly adjust the exercise load from the actual situation 0.1222

Teaching effectiveness 0.1899 Regulation ability The overall control ability of classroom 0.2364

Student performance The exertion of students’ subjective role 0.3576

Teach students in accordance with their aptitude The principle of scientific implementation and differential treatment 0.2692

Mission accomplished The tasks of teaching and education are completed timely and the effect is obvious 0.1368

Teaching characteristics 0.1213 Teaching method The teaching method has pertinence and novelty 0.3849

Teaching devices Teaching methods are diversified and targeted 0.3927

Content of courses The teaching content keeps pace with the times 0.2224

Primary indices	Two level index	Index connotation	Weight
Teaching preparation 0.1630	Preparation before class	The layout of field equipment is reasonable; the task of teaching plan meets the requirements of the plan	0.1289
	Task of teaching plan	The teaching task is clear, specific and comprehensive, and the teaching content meets the requirements of the task	0.4970
	Teaching plan content	The arrangement of teaching contents is reasonable and pertinent	0.1813
	Key points of teaching plan	The teaching content embodies the key and difficult points, and the load arrangement is reasonable	0.1928
Teaching organization 0.3371	Teaching method	Proper use of multimedia teaching means	0.2580
	Organizational process	The arrangement of teaching process is full of rhythm	0.3103
	Guidance technology	The explanation is concise, the demonstration is right, the instruction technique is just right	0.1355
	Teaching emphasis	The teaching emphasis and difficulty are prominent, and the purpose is strong	0.2962
Sports load 0.1887	Load content	The content of the load is purposeful, targeted, and selective	0.2523
	Load density	Conforms to the type of class and the characteristics of teaching materials	0.1725
	Load intensity	The amount, intensity and proper of the class exercise coincide with the teaching content	0.2216
	Load adjustment	Flexibly adjust the exercise load from the actual situation	0.1222
Teaching effectiveness 0.1899	Regulation ability	The overall control ability of classroom	0.2364
	Student performance	The exertion of students’ subjective role	0.3576
	Teach students in accordance with their aptitude	The principle of scientific implementation and differential treatment	0.2692
	Mission accomplished	The tasks of teaching and education are completed timely and the effect is obvious	0.1368
Teaching characteristics 0.1213	Teaching method	The teaching method has pertinence and novelty	0.3849
	Teaching devices	Teaching methods are diversified and targeted	0.3927
	Content of courses	The teaching content keeps pace with the times	0.2224

3.2 The establishment of teaching quality evaluation index system

Teaching preparation is the necessary preparatory work for teachers before conducting teaching activities. Only with clear plans, can teachers be methodical, so as to quickly enter the teaching state, and full of confidence in the teaching activities. Teaching preparation is the key prerequisite for the quality of a physical education class. If there is a problem in this premise, it will eventually lead to a reduction in the quality of teaching in physical education class. For the sports teaching, it refers to that according to the requirements of the society for the teaching of physical education and the characteristics of students’ physical and mental development, the physical education teacher guides the student to understand the sports item, grasps the sports related knowledge, the skill, and develops themselves through the teaching conditions such as field, equipment and so on. This process includes the teaching methods, means, contents and teaching organization of teachers. In the classroom teaching activities, organization teaching is the key evaluation index of teaching quality. Generally speaking, teaching effect is the result of teaching. It is the direct embodiment of the completion of the teaching plan and teaching objectives. For a high quality physical education, the teaching effect should be focused on the students’ attention, and the classroom atmosphere is more active. Students are more active in participation and students can master the basic knowledge of sports skills.

The results show that in the quality evaluation index system of public sports teaching in our school, the weights of the first grade indicators were arranged as teaching organization (0.3371), teaching effect (0.1899), exercise load (0.1887), teaching preparation (0.1630) and teaching characteristics (0.1213). The teaching organization ranked first in the ranking of the first level indicators, and the teaching effect ranked in the second place. The Reason of this conclusion is that in the school sports teaching reform, the evaluation standard of physical education teaching quality is more and more perfect, and it not only pays attention to the development of students themselves, but also focuses on the quality of teaching organization. It not only pays attention to the evaluation of teaching results, but also pays attention to the evaluation of the teaching process. In the teaching activities, it highlights the teaching guiding ideology of “people-oriented”. It also pays attention to the development of students’ personality and theformation of lifelong sports consciousness.

4 Comprehensive evaluation of teaching quality in physical education class

In order to make the teaching evaluation more reliable and accurate, the author made the evaluation model, as shown in Fig. 1 below. This model has many important functions: (1) It can calculate the comprehensive evaluation value of the evaluation object, and sort it reasonably. The comprehensive evaluation value covers the self-evaluation score of the students, which can reflect the teaching effect more systematically. (2) It gives the teaching evaluation feedback to the relevant personnel in the first time, which can make it clear about the weak links of teaching, and urge them to constantly optimize and improve the quality of teaching.

Fig. 1.

The Target High Dimensional Data Mode.

The highlight of the model lies in the evaluation method. This study combines the grey system theory with the degree of correlation theory to adjust and optimize the fuzzy comprehensive evaluation method. The so-called fuzzy comprehensive evaluation method refers to a comprehensive evaluation method based on fuzzy teaching on the evaluation object. This method adapts to the fuzziness of teaching phenomena and can collect all the opinions of the evaluators comprehensively. In the past, multiple targets and criterions often appear in the evaluation system. If you only use qualitative analysis and logical judgment, it will be difficult to obtain accurate analysis results. Now the analytic hierarchy process can be used to determine the weight value, which can effectively solve the above problems. When the correlation degree of all the factors in the system is analyzed, with the help of the grey relation degree method in grey system theory, the fuzzy comprehensive evaluation method can be optimized by combining the relation degree and the more reliable and effective results can be obtained, which avoids the occurrence of conclusion errors due to the principle of maximum membership degree. Therefore, this study combines the fuzzy comprehensive evaluation method and the grey system theory. The detailed teaching quality evaluation structure is as follows:

Set up the factor set, which is an index set composed of evaluation indexes: U = [u₁, u₂, ⋯ , u_n]

Set up the evaluation set, which is a collection of the quality of the evaluation target:C = [c₁, c₂, ⋯ , c_n]

The weight matrix of index is obtained by analytic hierarchy process (AHP):W = [W₁, W₂, ⋯ , W_n]. Among them, W₁ is the weight value of each index, and the consistency test is carried out to analyze its credibility according to (1) formula:

CR = C_{IN} / R_{IN}

Among them, C_IN is the evaluation consistency index of n order judgment matrix. R_IN is the average consistency index of n reciprocal matrix. When C_IN ≤ 0.10, it can be concluded that the evaluation is generally compatible and the analysis results are credible. On the contrary, it can be considered that the degree of evaluation inconsistency is high, and it is suggested to re-evaluate the evaluation.

Construct single factor evaluation matrix R, among them, R_i = [r₁₁, r₁₂, ⋯ , r_in] is the i-th factor evaluation results:

R = [\begin{matrix} r_{11} & r_{12} & \begin{matrix} \dots & r_{1 n} \end{matrix} \\ r_{21} & r_{22} & \begin{matrix} \dots & r_{2 n} \end{matrix} \\ \begin{matrix} \dots \\ r_{m 1} \end{matrix} & \begin{matrix} \dots \\ r_{m 2} \end{matrix} & \begin{matrix} \begin{matrix} \dots & \dots \end{matrix} \\ \begin{matrix} \dots & r_{mn} \end{matrix} \end{matrix} \end{matrix}]

Use weighted average comprehensive evaluation model

$A = W \cdot R = [W_{1}, W_{2}, \dots, W_{n} [\begin{matrix} r_{11} & r_{12} & \begin{matrix} \dots & r_{1 n} \end{matrix} \\ r_{21} & r_{22} & \begin{matrix} \dots & r_{2 n} \end{matrix} \\ \begin{matrix} \dots \\ r_{m 1} \end{matrix} & \begin{matrix} \dots \\ r_{m 2} \end{matrix} & \begin{matrix} \begin{matrix} \dots & \dots \end{matrix} \\ \begin{matrix} \dots & r_{mn} \end{matrix} \end{matrix} \end{matrix}]$

Calculate grey correlation degree and determine association order

\begin{matrix} ε_{i}^{(k)} = (\min_{i} \min_{k} | x_{0}^{(k)} - x_{i}^{(k)} | + 0.5 \max_{i} \max_{k} | x_{0}^{(k)} - x_{i}^{(k)} |) / \\ (x_{0}^{(k)} - x_{i}^{(k) + 0.5} \max_{i} \max_{k} | x_{0}^{(k)} - x_{i}^{(k)} |) \end{matrix}

$r_{i} = \frac{1}{N} \sum_{k + 1}^{n} ɛ_{i}^{(k)}$ , where $ɛ_{i}^{(k)}$ is correlation coefficient; R_iis correlation degree; 0.5 is the resolution coefficient; $\min_{i} \min_{k} | x_{0}^{(k)} - x_{i}^{(k)} |$ is the minimum difference of two levels. The first level of desertion is for k, traversing k to take the minimum. The second level of desertion is for i, traversing i to take the minimum. $\max_{i} \max_{k} | x_{0}^{(k)} - x_{i}^{(k)} |$ is the maximum difference of two levels. The first level of desertion is for k, traversing k to take the maximum. The second level of desertion is for i, traversing i to take the maximum.

5 Comprehensive evaluation of teaching quality in physical education

5.1 Application examples

This paper takes the evaluation of classroom teaching of Public Physical Education in our school in the last semester of 2017 as an example, and uses the above methods and models to evaluate the quality of classroom teaching. 3 were randomly selected from a total of 5 experts to assess.

Set up the factor set: U = [u_1/ Lesson preparation, u_2/ Class process, u_3/ Lesson effect, u_4/ End of class]

Set up evaluation sets and assign C = [optimal, good, medium, poor, inferior]

Use AHP method to determine the index weight. On the basis of consulting experts’ opinions, the corresponding judgment matrix is established by using the 1–9 scale method, and the characteristic equation is determined to determine the weight of each factor at the same level.

|λ_I-A|=0, then λ_max=4.145978. It is brought into the characteristic equation and the corresponding homogeneous linear equations are obtained:

x¹ = 0.1630 x² = 0.3371 x³ = 0.1887 x⁴ = 0.1899 x⁵ = 0.1213

The consistency test showed: CR = 0.0361<0.1. It is concluded that the evaluation results are generally consistent and the analysis results are credible, and the weight sets of each factor of the evaluation index are obtained: $W = [0.1630, 0.3371, 0.1887, 0.1899, 0.1213]$ (19)

The expert group evaluated 3 teachers, and the single factor evaluation matrix R was:

$R_{1} = | \begin{matrix} 0.1 & 0.2 & \begin{matrix} 0.4 & 0.2 & 0.1 \end{matrix} \\ 0.2 & 0.3 & \begin{matrix} 0.4 & 0.3 & 0.1 \end{matrix} \\ \begin{matrix} 0.2 \\ 0.1 \\ 0.2 \end{matrix} & \begin{matrix} 0.5 \\ 0.2 \\ 0.3 \end{matrix} & \begin{matrix} \begin{matrix} 0.2 & 0.1 & 0.2 \end{matrix} \\ \begin{matrix} 0.4 & 0.3 & 0.1 \end{matrix} \\ \begin{matrix} 0.5 & 0.1 & 0.1 \end{matrix} \end{matrix} \end{matrix} |$ $R_{2} | \begin{matrix} 0.2 & 0.4 & 0.3 & 0.1 & 0.2 \\ 0.2 & 0.3 & 0.4 & 0.1 & 0.1 \\ 0.5 & 0.3 & 0.1 & 0.1 & 0.2 \\ 0.2 & 0.4 & 0.2 & 0.1 & 0.1 \\ 0.1 & 0.5 & 0.2 & 0.2 & 0.3 \end{matrix} |$

$R_{3} | \begin{matrix} 0.1 & 0.3 & 0.3 & 0.2 & 0.1 \\ 0.3 & 0.3 & 0.2 & 0.2 & 0.1 \\ 0.4 & 0.3 & 0.2 & 0.1 & 0.1 \\ 0.1 & 0.3 & 0.2 & 0.3 & 0.1 \\ 0.3 & 0.2 & 0.4 & 0.1 & 0.1 \end{matrix} |$

The weighted average comprehensive evaluation model and fuzzy matrix synthesis operation are used to get the evaluation results

$\begin{matrix} A_{1} = w \cdot R_{1} = W \\ = [0.1630, 0.3771, 0.1887, 0.1899, 0.1213] \cdot R_{1} \\ = | \begin{matrix} 0.1 & 0.2 & \begin{matrix} 0.4 & 0.2 & 0.1 \end{matrix} \\ 0.2 & 0.3 & \begin{matrix} 0.4 & 0.3 & 0.1 \end{matrix} \\ \begin{matrix} 0.2 \\ 0.1 \\ 0.2 \end{matrix} & \begin{matrix} 0.5 \\ 0.2 \\ 0.3 \end{matrix} & \begin{matrix} \begin{matrix} 0.2 & 0.1 & 0.2 \end{matrix} \\ \begin{matrix} 0.4 & 0.3 & 0.1 \end{matrix} \\ \begin{matrix} 0.5 & 0.1 & 0.1 \end{matrix} \end{matrix} \end{matrix} | \\ = [0.1647, 0.3025, 0.3070, 0.5151, 0.1189] \end{matrix}$ Similarly, A₂ = w · R₂ = [0.2445, 0.3596, 0.2649, 0.161, 0.1594] $A_{3} = w \cdot R_{3} = [0.2483, 0.2897, 0.2486, 0.2759, 0.1]$

Find the grey correlation degree and determine the association order

Firstly, the initial value of Ai is processed: ${\overset{´}{A}}_{1} = [1, 1.8367, 1.8640, 3.1275, 0.7219]$ ${\overset{´}{A}}_{2} = [1, 1.4780, 1.0834, 0.4748, 0.6519]$ ${\overset{´}{A}}_{3} = [1, 1.1595, 1.0015, 1.1112, 0.4027]$ $\min_{i} \min_{k} | x_{0}^{(k)} - x_{i}^{(k)} | = 0$ $\max_{i} \max_{k} | x_{0}^{(k)} - x_{i}^{(k)} | - 2.6527$

When A₁ is the eigenvalue of the system,

Formula of correlation coefficient: $\begin{matrix} ε_{i}^{(k)} = \frac{\min_{i} \min_{k} | x_{0}^{(k)} - x_{i}^{(k)} | + 0.5 \max_{i} \max_{k} | x_{0}^{(k)} - x_{i}^{(k)} |}{x_{0}^{(k)} - x_{i}^{(k) + 0.5} \max_{i} \max_{k} | x_{0}^{(k)} - x_{i}^{(k)} |} \\ = \frac{1.32635}{Δ_{i} (k) + 1.32635} \end{matrix}$

Correlation formula is $r_{i} = \frac{1}{N} \sum_{K + 1}^{n} ε_{i}^{(k)}$ , The correlation results for ${\overset{´}{A}}_{1}$ is $r_{{\overset{´}{A}}_{2}} = 0.7391, r_{{\overset{´}{A}}_{3}} = 0.6941$ .

Similarly, when A₂ is the eigenvalue of the system,

When A₃ is the eigenvalue of the system, $r_{{\overset{´}{A}}_{1}} = 0.6460, r_{{\overset{´}{A}}_{2}} = 0.8027$

Then, $r_{{\overset{´}{A}}_{1}} max (0.7391, 0.6460) = 0.7391$ $r_{{\overset{´}{A}}_{2}} max (0.7391, 0.8207) = 0.7391$ $r_{{\overset{´}{A}}_{3}} max (0.6491, 0.8538) = 0.8538$

That is, the ranking of 3 teachers’ classroom teaching quality is: Teacher 3>Teacher 2 >Teacher 1 This is consistent with the qualitative evaluation of the lectures in the group of experts in daily teaching. This shows that the fuzzy comprehensive evaluation method is improved by using the grey relational grade, which avoids the disadvantages of adopting the principle of maximum membership degree. Therefore, this evaluation method can be used in the evaluation of public sports teaching in Colleges and universities. However, the shortcomings of the evaluation method are that the calculation process is complicated. The following work of this study is to program the evaluation process by computerprogramming.

5.2 Recommendations

The evaluation of teaching quality evaluation is a multifaceted process. In the process of evaluation, the quality of teaching cannot be judged according to the results of one-sided evaluation, and effective evaluation methods should be adopted according to the actual situation of colleges and universities to carry out reasonable and targeted evaluation.

Teaching evaluation mainly includes two aspects: expert evaluation and student evaluation. Based on the current requirements of quality education, we should adhere to the people-oriented teaching idea, and then attach importance to the student evaluation in the process of teaching evaluation. A perfect evaluation system should include the evaluation indexes of all aspects of the evaluation target, so the index set of the public sports teaching quality evaluation system should be expanded constantly.

The teaching quality evaluation index system is a system, including expert evaluation and student evaluation, and the two influence each other. In the construction of evaluation index system, we should allocate the two indicators at the same time, avoid unfair phenomenon, increase the proportion of students’ evaluation, and make the whole index system become human nature reasonable.

In the teaching of public physical education, the quality evaluation system of public physical education is used and developed, and the system will be perfected in the future. In the practice teaching activities, the evaluation index which suitable for the public body teaching is added to the index concentration.

6 Conclusion

China’s education reform is being carried out like a raging fire. The reform of educational concept and educational model has become the focus of attention, but the research on educational evaluation is not deep enough, especially the evaluation of classroom teaching quality. In collecting evaluation information, defining the index system and formulating evaluation standards, it seems too casual, which does not systematically carry out relevant work. So that the reliability of evaluation results is lower. At the same time, we should continue to optimize and adjust the technical classroom teaching index system by using the evaluation method mentioned in this study. Therefore, this system has higher pertinence. In addition, the weight of evaluation factors should be defined so that the accuracy of the evaluation results can be effectively ensured. And the objective and impartial position should be taken in the collection and collation of evaluation information. Frequency of attending lectures of experts, peers and related leaders should be up to the standard, so as to understand the teaching materials of teachers. In the process of evaluation, we should pay close attention to all factors, to ensure the evaluation of the fairness and rationality, so as to effectively promote the reform of teaching, to further improve the quality of teaching effect of public sports class.

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