1 Introduction

The number of administrative departments of the government continues to merge with the reform of the government system and the development of the economy. No matter whether the scale of government administration is large or small, it is necessary to manage the performance of administrative staff. There are some difficulties in this part of the management. The administrative department of government is a non-profit organization. Under the situation of the reform of the government system and mechanism, its business scale is expanding constantly. The staff in the administration include the office, financial, and other aspects. Administrators, like staff in other departments, put the goals and interests of the executive branch at the top of their work. The performance management of administrative staff plays an important role in the development of administrative staff as well as the whole government administratio n[1]. Fuzzy normal form neural network partly covers the basic knowledge of neural computation and fuzzy neural computation, and the realization of the algorithm can identify the essence of the relationship between the fuzzy system and neural network. The work of administrative staff is complicated, flexible, and difficult to quantify. Administrative staff provides more temporary services to other departments, such as manpower and finance. These temporary services are not easy to judge in quantitative management. The work of administrative personnel is complex and often receive other tasks in the work [2]. Fuzzy normal form system can provide big data support for medical health and reliable data source for decision-makers. In this paper, prov-s, safety data origin model based on W3CPROV, is proposed to study various labeled objects in the safety origin relation graph and define the range of related objects. Compared with the task of the production department, the work of the administrative staff is not restricted and directed by the production plan, and there is often sudden work in the daily work. This kind of sudden work can account for a large part of the total work of administrative personnel. The administrative personnel’s work is too dynamic, and the examination will encounter problems of one kind or another [3].

The administrative staff’s work content is more complex, mainly for the other departments of the government administrative department to provide services and help, and it also has the function of supervision and coordination [4]. The performance assessment of the administrative staff is not enough, and the quantitative process and the quantitative results are not clear and accurate. In the performance assessment of the administrative staff, the evaluation index is not flexible and does not take into account the differences between the administrative staff. Although the use of the unified assessment can save the cost for the government administration, it will strike the enthusiasm of the administrative staff [5]. Therefore, it needs to be studied. This paper proposes an effective performance evaluation model for government administrators. This paper puts forward the performance evaluation model of government administrators based on an analytic hierarchy process and combines the results of a descriptive statistical average analysis to test the sample regression of the large data of the performance evaluation of the government administrators and adopt the adaptive fuzzy scheduler. The law carries out the classification and recognition of the performance data of the government administrators [6]. According to the results of the performance information fusion of the government administrative personnel, the hierarchical analysis is carried out, the quantitative evaluation model of the performance of the administrative personnel of the government is established, and the regression analysis and adaptation of the administrative personnel management of the government are carried out by the F statistics analysis method. The adjustment, based on the hierarchical statistical analysis results of adaptive adjustment of government administrative personnel, combined with the AHP method, is to achieve the performance evaluation of government administrative personnel optimization. Finally, the empirical analysis of the performance test is taken, and it shows the superiority of this model in improving the ability of the performance evaluation of administrative personnel of the government [7, 8].

The rest of this paper is organized as follows. Section 2 discusses the statistical analysis model and constraint parameter analysis of the performance evaluation of government administrators, followed by optimization of the performance evaluation model for government administrators in Section 3. Empirical analysis and test are discussed in Section 4. Section 5 concludes the paper with a summary and future research directions.

2 Statistical analysis model and constraint parameter analysis of the performance evaluation of government administrators

2.1 Statistical analysis model of performance evaluation of government administrators

Performance management is a kind of concept put forward in the 1970s. Since it was put forward, all walks of life have carried on the thorough discussion to the performance management. In the 1990s of the last century, the theory of performance management matured gradually. In essence, performance management is a representative of ideas and concepts, and a series of problems related to enterprise performance are systematically considered around how to develop and operate effectively. Performance management involves enterprise planning, strategy, organization, strategic development, motivation, and leadership. Government administration is an organization that plays the role of guarantee and service in the management system, and it is also the organization that exerts the organizational function and the leading function. Therefore, the administration of the government to the top and bottom of the business activities, capital management, and other implementation coordination [9, 10].

First of all, it is necessary to construct the data sampling information flow model of government administrators’ performance evaluation and combine the statistical characteristic analysis and descriptive statistical decision analysis method to model the performance evaluation of government administrators [11,12,13]. According to the above analysis, the overall implementation process of performance evaluation modeling of government administrators based on AHP is shown in Fig. 1.

Fig. 1
figure 1

Overall implementation process of performance evaluation modeling for government administrators based on AHP

The nonlinear statistical feature sequence analysis method is used to analyze the characteristics of the performance evaluation modeling data of the government administrators and the statistical modeling [14,15,16]. Firstly, the original data collection of the performance of the government administrators is carried out. By using the principal component characteristic analysis model method of the performance evaluation of the government administrative personnel, the regression test model of the performance evaluation model of the government administrative personnel is expressed as follows:

$$ {G}_i=\sum \limits_j{\alpha}_j{y}_i{y}_jK\left({x}_i,{x}_j\right)+{y}_ib-1 $$
(1)

Combined with the auto-regressive moving average (ARMA (p, q)) model for descriptive statistical analysis of large data government administrative personnel management effectiveness of the government administrative personnel to the statistical performance evaluation model for distribution, the equation is as follows:

$$ {x}_n={\varphi}_0+\sum \limits_{i=1}^p{\varphi}_i{x}_{n-i}+\sum \limits_{j=0}^q{\theta}_j{\eta}_{n-j} $$
(2)

In which, {ηi} is the mean value of 0, the variance is σ2, and φ0, φ1, φ2, ⋯φp is the performance correlation distribution data of the government administrators. θ1, θ2, ⋯θq is called the descriptive statistical average coefficient of the government administrative staff management, and the statistical analysis method is used to match the characteristics. According to the statistical results of the above sample descriptive statistical analysis, the performance evaluation model of government administrators is established under the model of AHP [17,18,19].

2.2 Analysis of the explanatory variables of the performance evaluation of government administrators

On the basis of big data analysis of government administrative personnel management, the optimal design of the performance evaluation model of government administrative personnel is carried out, and a performance evaluation model of government administrative personnel based on hierarchical analysis is proposed in this paper. Combining the results of descriptive statistical average analysis, the regression test of the performance evaluation of government administrators is carried out, and the test statistics are obtained:

$$ Q=\frac{C_1\sum \limits_{i=1}^k\exp \left[-{S}_2{\left({V}_i-\mu \right)}^2\right]}{1+\exp \left[-{S}_1\sum \limits_{i=1}^k{w}_i\left({T}_i-{V}_i\right)\right]} $$
(3)

In which, C1, S1, and S2 are constant, indicating the decision-making statistical parameters of the performance of government administrators. By using F test method, the characteristic statistical function of the optimal government administrators’ performance decision is recorded as follows:

$$ S\left(i,j\right)=\frac{\sum_{u\in {U}_{ij}}\left({V}_{u,i}-3\right)\left({V}_{u,j}-3\right)}{\sqrt{\sum_{u\in {U}_{ij}}{\left({V}_{u,i}-\overline{V_{.i}}\right)}^2}\sqrt{\sum_{u\in {U}_{ij}}{\left({V}_{u,j}-\overline{V_{.j}}\right)}^2}} $$
(4)

The adaptive fuzzy scheduling method is adopted to classify and identify the performance data of the government administrators, and the recognition function is expressed as follows:

$$ \underset{\omega, h,{\zeta}_l,{\zeta}_l^{\ast }}{\min }=\frac{1}{2}{\omega}^T\omega +c\sum \limits_{i=1}^l\left({\zeta}_l+{\zeta}_l^{\ast}\right) $$
(5)

A hierarchical analysis and quantitative evaluation model of the performance of government administrators is established [20, 21]. Combined with the method of information fusion, the statistical distribution model of the optimal performance of government administrators is obtained as follows:

$$ Sn=\frac{\sum_i^n{\max}_{j=1}^m{t}_{ij}}{\sum_{i=1}^n{n}_i} $$
(6)
$$ PPV=\frac{\sum_{j=1}^m{\max}_{i=1}^n{t}_{ij}}{\sum_{j=1}^m{\sum}_{i=1}^n{t}_{ij}} $$
(7)

According to the results of descriptive statistical analysis, the effectiveness of the management of government administrators is evaluated, and a quantitative evaluation model of the performance of government administrators is established [22, 23].

3 Methods

3.1 Construction of performance evaluation index of government managers

The establishment of the evaluation index system is the basic condition to complete the performance evaluation of government managers. Constructing a scientific and effective evaluation index system needs the process of index primary selection, perfection to the final use, and so on [24, 25]. The design of evaluation index system should follow the basic principles of “purpose, science, applicability, maneuverability, guidance, and credibility.” According to the current evaluation criteria of cadres in our country, that are “ability, moral character, diligence, performance” standard, and combined with the actual work requirements of government administrators, this paper selects the following performance appraisal evaluation index system, including “Ability, Moral character, Performance, and Diligence,” the four first-degree indicators [26, 27]. The specific meaning of the whole performance evaluation index system and its various indicator systems is shown in Table 1.

Table 1 Performance evaluation indicators for government managers

According to the survey of issuing the above indicators, this paper gives weight to each index of the performance evaluation of government management personnel and constructs the judgment matrix by using the weighted average summation method. The sum-product method is used to determine the weight coefficient of each judgment matrix [28, 29]. Finally, through consistency detection, the detection process is as follows:

The processing results of the judgment matrix c are shown in Table 2.

Table 2 Judgment matrix B-C

Judgment matrix D-E processing results are shown in Table 3.

Table 3 Judgment matrix D-E

3.2 AHP model for performance evaluation.

Based on the above evaluation indicators, a performance evaluation model of government administrators is proposed based on AHP, establishes a quantitative evaluation model of hierarchical analysis and performance of government administrators, and adopts F statistical analysis method to carry out government performance evaluation [30]: regression analysis and adaptive adjustment of administrative staff management, establishment of quantitative evaluation model of financial expenditure and performance of government administrators, adjustment of financing structure using F statistic analysis method, administration based on AHP, and the fuzzy comprehensive decision function of the performance evaluation of the administrative personnel of the government [31, 32]:

$$ {\mu}_{B_i}={a}_{B_i}+{b}_{B_i}\Delta +{c}_{B_i}\Phi $$
(8)

In which, \( {a}_{B_i}=\frac{B_i}{B_U+{B}_v} \), \( {b}_{B_i}=\frac{\left({B}_U-{B}_i\right)\left({B}_i-{B}_v\right)}{\left({B}_U+{B}_v\right){B}_i} \), and \( {c}_{B_i}=\frac{B_U{B}_v}{\left({B}_U+{B}_v\right){B}_i} \). According to the correlation analysis of the linear fitting results of the performance evaluation of the government administrative personnel, the linear fitting formula is expressed as follows:

$$ f(x)=\sum \limits_{i=1}^l\left({a}_i+{a}_i^{\ast}\right)k\left(x-{x}_i\right)+b $$
(9)

According to the performance information fusion results of government administrators, the hierarchical analysis is carried out, and the constraint rules of performance evaluation are expressed as follows [33, 34]:

$$ \min (f)=\sum \limits_{i=1}^m\sum \limits_{j=1}^n{C}_{ij}{X}_{ij} $$
(10)
$$ \mathrm{s}.\mathrm{t}\left\{\begin{array}{l}\sum \limits_{j=1}^m{X}_{ij}={a}_i,i=1,2\cdots m\\ {}\sum \limits_{i=1}^m{X}_{ij}={b}_i,j=1,2\cdots n\\ {}{X}_{ij}\ge 0,i=1,2\cdots m,j=1,2\cdots n\end{array}\right. $$
(11)

According to the above analysis, the adaptive fuzzy scheduling method is used to mine and evaluate the big data performance of government administrators.

3.3 Quantitative evaluation of the performance of government administrators

By using F statistic analysis method, the regression analysis of government administrative personnel management is carried out, and the pre-progressive weighting coefficient of performance evaluation is obtained as follows:

$$ {CW}_{\mathrm{min}}^n=\left\{\begin{array}{l}\left(\left(1-{B}_{l(n)}\right){e}^{1-{\alpha}_n}+{B}_{l(n)}\right)\times {CW}_{\mathrm{min}}^{l(n)},{\alpha}_n>1\\ {}{CW}_{\mathrm{min}}^{l(n)},\kern8.399996em 0\le {\alpha}_n\le 1\end{array}\right. $$
(12)
$$ {B}_{l(n)}={\left(1/\left(1+{\overline{D}}_{l(n)-1}\right)\right)}^{\chi } $$
(13)
$$ {\alpha}_n=\left\{\begin{array}{l}\left|{D}_n\right|/\left({\overline{D}}_{l(n)}\right),{\overline{D}}_{l(n)}\ne 0\\ {}0,\kern4.699998em {\overline{D}}_{l(n)}=0\end{array}\right. $$
(14)

In which, αn is the asynchronous iterative coefficient of the performance evaluation of the government administrators, and Bl(n) is the error adjustment coefficient of the performance evaluation of the government administrators:

$$ {\left(1+\overline{D}\right)}^M>1 $$
(15)
$$ A/{CW}_{\mathrm{min}}^0>1 $$
(16)

Combined with the analytic hierarchy process, the gray scale quantification coefficient of the performance evaluation is satisfied:

$$ \chi >0 $$
(17)

If \( {\left(1+\overline{D_{l_i}}\right)}^{\chi }>1 \), the performance evaluation characteristics of the output meet the following requirements:

$$ {CW}_{\mathrm{min}}^{l_{i+1}}>{CW}_{\mathrm{min}}^{l_i} $$
(18)

Because

$$ 0<\left(1-{B}_{l(n)}\right){e}^{1-{\alpha}_n}<1-{B}_{l(n)} $$
(19)
$$ {B}_{l(n)}<\left(1-{B}_{l(n)}\right){e}^{1-{\alpha}_n}+{B}_{l(n)}<1 $$
(20)

Thus, the time inversion statistical correlation coefficient of the performance evaluation modeling of government administrators is obtained as follows:

$$ \left(\left(1-{B}_{l(n)}\right){e}^{1-{\alpha}_n}+{B}_{l(n)}\right)\times {CW}_{\mathrm{min}}^{l(n)}>{CW}_{\mathrm{min}}^{l(n)-1} $$
(21)

While αm > 1, then:

$$ {CW}_{\mathrm{min}}^{l(n)}>{CW}_{\mathrm{min}}^{l(m)}>{CW}_{\mathrm{min}}^m $$
(22)

While αm ≤ 1时, then:

$$ {CW}_{\mathrm{min}}^n={CW}_{\mathrm{min}}^{l(n)}>{CW}_{\mathrm{min}}^{l(m)}={CW}_{\mathrm{min}}^m $$
(23)

The convergence function of performance evaluation satisfies:

$$ {CW}_{\mathrm{min}}^n>{CW}_{\mathrm{min}}^m $$
(24)

It can be seen that the statistical characteristic quantity of performance evaluation is greater than the threshold value, and the performance evaluation model of government administrators constructed in this paper is bounded convergent.

4 Experiment

The experiment adopts Matlab 7, the method of sampling the data of government administrative personnel’s performance evaluation modeling adopts the method of social investigation and descriptive statistical analysis. The software of data analysis is SPSS 19.0. The basic statistical results of the personnel are shown in Table 4. Figure 2 is the distribution diagram of network nodes.

Fig. 2
figure 2

Network node distribution diagram

Table 4 Basic information of government administrators
Table 5 Regression model coefficient table for performance evaluation

According to the above descriptive statistical analysis results, the regression analysis of performance evaluation is carried out, and the results of regression analysis are shown in Table 5. Figure 3 shows the variation of latency with the network size.

Fig. 3
figure 3

Time-varying graph of the network size

According to the results of the regression analysis of performance evaluation in Table 5, the performance evaluation of government administrators is carried out. The distribution of the evaluation curve is shown in Fig. 4, taking the satisfaction degree of the masses and administrative behavior as the parameter.

Fig. 4
figure 4

Results of statistical analysis of performance evaluation of government administrators

The analysis shows that the performance evaluation of government administrators by using this model is accurate and the confidence level is better.

In order to further verify the effectiveness of the performance evaluation model of this paper, the quantitative evaluation method, the relative evaluation method, and the scale evaluation method are compared, as shown in Fig. 5.

Fig. 5
figure 5

Performance measurement comparison of different methods. a Quantitative evaluation method. b Relative evaluation method. c Scale evaluation method. d The proposed method

5 Results and discussion

In this paper, a performance evaluation model of government administrators based on AHP is proposed. Combined with the results of descriptive statistical average analysis, the sample regression test of big data performance evaluation of government administrators is carried out, and the adaptive fuzzy scheduling method is used to classify and identify the performance big data of government administrators. According to the results of the performance information fusion of government administrators, the hierarchical analysis and the quantitative evaluation model of the performance of government administrators are established. The F statistic analysis method is used for the regression analysis and adaptive adjustment of the government administrative personnel management, and the adaptive adjustment for the government administrative personnel is carried out according to the results of the hierarchical statistical analysis, and combined with the AHP method, the performance evaluation and optimization of government administrators is realized. The results of the empirical analysis show that the performance evaluation of government administrators by using this method has higher accuracy, higher efficiency of big data processing, and better integration. This method has a good application value in the performance evaluation of government managers.