# The Application of Grey Relational Analysis in the Evaluation of Financial Auditing Effect and Improvement

Authors: Dongliang Wang
Journal: Mobile Information Systems
 (2022)

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## Abstract

Financial institutions are confronting more complicated risks as a result of the current financial crisis. Financial auditing is an essential aspect of government auditing since it serves to protect the security and stability of the national financial system by evaluating financial systemic vulnerabilities. Therefore, this paper combines the grey relational analysis to carry out research work on the financial auditing effect and improvement evaluation. Firstly, we conducted a preliminary selection of relevant financial audit impact indicators and identified the design of the influencing factor system as well as appropriate data for the influencing factors, resulting in the first evaluation system of the evaluation indicators. Secondly, we created a factor set for evaluating the financial audit improvement effect. The completed task proportion component and the task completion quality factor are the two kinds of improvement impact evaluation factors. On this foundation, this research develops a grey correlation-based assessment model for audit effect enhancement. The residual graph fitting findings indicate that the scheme has a good implementation impact and may be utilised to assess the financial auditing improvement effect.


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## Body

## 1. Introduction

Due to the numerous investment options available in the financial markets, numerous factors affecting investors’ decisions, and frequent dynamic changes in the markets, portfolio selection has become a particularly challenging process in portfolio management. Audit supervision aids in the consolidation of political power and can give institutional assurance for government function change. The national political system’s audit monitoring system is a necessary and vital component [1, 2]. By autonomously exercising the audit supervision authority, the audit institution is responsible for ensuring the successful execution of numerous state policies as well as the healthy and safe functioning of the state machinery [3]. Auditing contributes to the establishment of a full incentive, innovation, and restriction system by performing its tasks of supervision, service, attestation, assessment, consultation, and control [4, 5]. Financial institutions can use this mechanism to exercise their proper autonomy, increase the efficiency of financial resource allocation, and optimize the overall function of the financial ecological environment [6].The essence of audit is the “immune system” of economic and social operation, which plays the role of preventing, revealing, and resisting obstacles, contradictions, and risks in economic and social operation. Maintaining national security is the first priority of audit work [7, 8]. Similarly, the first priority of financial auditing is to maintain national financial security, which is also a higher requirement for financial auditing under the new situation. Some scholars believe that the first priority of financial auditing is to maintain national financial security and to play the “immune system” function [9]. Through auditing, we can be the first to feel the problem, we must find the problem earlier when it appears and work hard to prevent the occurrence of major problems or the accumulation of deep-seated conflicts, which is forward-looking [10–12]. Taylor and Baker found a significant positive correlation between the size of listed companies and the complexity of their business on audit fees through their research on British listed companies’ audit fees [13]. Francis found through his research on the Australian audit market that the size of company assets is an important factor affecting audit fees. At the same time, the number of subsidiaries of listed companies and the size of accounting firms have a great relationship with audit fees, and there is a significant positive correlation [14].It can comprehend the major contradiction and the key features of the contradiction and represent the correctness, by disclosing the deep-seated contradictions and lingering difficulties that exist in the current economic and financial operation process. Accounting firms with industry expertise earn more additional income than other accounting firms, according to Wang et al. research on Chinese data, and accounting firms can enter an industry by reducing audit fees to gain professional experience and win more clients later [15]. Furthermore, to address difficulties scientifically, we must devote significant time to the study and investigation of contradictions and problems, as well as to the solution of big problems in the actual world [16, 17]. In addition, practical audit recommendations or actionable policy recommendations to resolve conflicts and problems should be put forward.In this study, we use grey relational analysis to conduct financial auditing effect and improvement assessment research. Empirical research on audit fees and audit quality of financial companies is used to determine where financial firms’ risk emphasis originates [18–20]. However, because empirical research on financial sector audit-related issues is still in its infancy, empirical research on financial enterprise auditing quality is of tremendous practical importance. We created an audit impact improvement evaluation model based on grey correlation by constructing the initial evaluation system of the evaluation index and the set of improvement effect evaluation parameters.


## 2. Financial Audit Influence Index System Based on Entropy Weight Method

The building of the influencing factor system and the identification of the relevant data of the influencing factors are the first steps in selecting the influencing factors of the relevant indicators of the financial auditing effect. The first assessment system of the evaluation index is the influencing factor system utilised in model preparation [21, 22]. The qualitative factors can be evaluated by experts among the eight evaluation factors: the degree of development of the audit task area, the density of audit points around the task, the density of auditors around the task, the number of tasks, the difficulty of the task, the urgency of the task, the density of the number of audit cases, and the specified time.Scores and questionnaires can be obtained, and quantitative factors can be obtained by referring to relevant literature [23, 24]. Qualitative factors correspond to the quantitative values of fuzzy scoring as shown in Table 1.Table 1
Qualitative factor fuzzy numerical quantification table.
Qualitative description12345Data valueSmall/lowSmaller/lowerGenerallyBigger/higherLarge/highThe data of the influencing factors of audit tasks are obtained by referring to the literature, and the qualitative factors are fuzzy and quantitatively analyzed. The original data information of the construction standard evaluation is shown in Table2.Table 2
Original data table of influencing factors.
c1c2c3c4c5c6c7c8u12.422.342.514.964.254.34256424u21.631.581.695.012.854.85245824u32.212.142.295.146.215.33267924...........................U988.227.838.407.327.319.05328910U998.347.958.529.447.826.8433566U1008.568.168.748.057.278.4134526The relationship between the three indicators and eight factors, including the infrastructure construction in the audit area, the distribution of auditors, and the standard of task requirements, should be standardized and dimensionless before the correlation analysis. Correlation analysis was performed on the processed Table2 to obtain the corresponding relationship between the indicators and factors. Table 3 shows the correspondence table of three indicators and eight factors.Table 3
Correspondence table of three indicators and eight factors.
c1c2c3c4c5c6c7c8x10.3230.4490.218−0.215−0.314−0.4150.201−0.394x20.1790.1530.6320.3560.2890.2160.5870.256x3−0.103−0.215−0.4950.6850.7690.854−0.5130.812According to the equal interval method, the values of the influencing factors in the information table are discretized, and the 8 groups of data are all discretized according to the discretization standard.(1)k=10≤k≤0.333,20.333≤k≤0.666,30.666≤k≤1..According to the general reduction method, the influencing factors in the information table are reduced. From the above-mentioned discrete table of influencing factor data, it can be obtained,(2)INDC=INDc1,c2,c3,…,cn=c1,c2,c3,...,cn.Therefore, the reduced information table is obtained, as shown in Table4.Table 4
Correspondence table after reduction.
c1c2c3c4c5c6x10.3230.4490.218−0.215−0.314−0.415x20.1790.1530.6320.3560.2890.216x3−0.103−0.215−0.4950.6850.7690.854Substitute the number of reduction setsK, the number k of reduction sets with relatively important attributes gj and the above-related data into the following formula:(3)wgj∗=kK,wgj1=wgj∗∑j∈Nwgj∗.The weight to determine the final audit effect affected byc1,c2,c3,c4,c5,c6 is(4)wgj1=0.235,0.146,0.157,0.168,0.119,0.175.On the basis of considering the amount of information of relevant factors and considering the importance of factors to the quality of the task, for this reason, combined with the entropy weight method to improve, so as to determine more true and comprehensive weights.First, six evaluation indicators were determined, which were the development level of the audit task area, the density of audit points around the task, the number of auditors around the task, the amount of tasks, the difficulty of the task, and the urgency of the task. The 6 indicators are represented byX1,X2,⋯,Xk here, among which Xi=x1,x2,⋯,xnn=22. The normalized value of each indicator data is Y1,Y2,⋯,Yk . Then, we obtain the following equation:(5)Yij=Xij−minXimaxXi−minXi.According to the definitionpij=Yij/∑i=1nYij of information entropy in information theory, the information entropy of a set of data is among them, if pij=0, then define,(6)limpij⟶0pijlnpij=0.According to the calculation formula of information entropy, the information entropy of each indicator is calculated asE1,E2,⋯,Ek. The weight of each indicator is calculated through information entropy.(7)Wi=1−Eik−∑Eii=1,2,⋯,k.We use MATLAB programming to calculate the impact weight of six indicators and obtain the audit task area development degree, the density of audit points around the task, the density of auditors around the task, the amount of tasks, the difficulty of the task, and the urgency of the task. The weight of the audit effect iswgi=0.234,0.146,0.158,0.168,0.119,0.175.


## 3. Financial Audit Improvement Effect Evaluation Factor Set

The improvement effect of financial auditing needs to consider the proportion and quality of completed audit tasks, so the evaluation factors can be divided into two categories: the proportion of completed tasks and the quality of task completion [25, 26]. The fraction of completed job points is the task density, auditor density, and scheduled task quota, according to a literature study and statistical analysis of issue data [27, 28]. The job completion quality criteria are derived based on the current literature and data as the auditor's reputation value, the scheduled task start time, and the task price.The allocation of the first-level assessment model is difficult to fairly perfect since there are numerous factors impacting the proportion of completed task points, and the types are diverse. As a result, a second-level fuzzy comprehensive assessment model is created, with the above factors serving as the foundation for two first-level factor sets.(8)C1=D1,D2,D3,C2=E1,E2,E3.Here,C1 is the proportion factor of completed task points, C2 is the completion quality factor of task points, and two first-level factor sets constitute a second-level factor set. Known factor set U and evaluation set V. The hierarchical structure diagram of the two-level fuzzy comprehensive evaluation model we constructed is shown in Figure 1.Figure 1
Hierarchical structure diagram of the second-level fuzzy comprehensive evaluation model.The key to fuzzy comprehensive assessment is the description of the factor membership degree. By creating a membership function and inserting it into the measured value, the membership degree may be computed.We use the analytic hierarchy process to combine the expert scoring process with the mathematical model constructed by fuzzy synthesis to obtain the weight value of each factor. The eigenvalues and eigenvectors are calculated using the summation method. The weight calculation results are shown in Table5.Table 5
Weights of each evaluation factor.
CategorySecondary weightFactorPrimary weightThe proportion of completed tasks C10.651Task density D10.423Personnel density D20.328Scheduled task quota D30.249Mission completion quality C20.349Personnel reputation value E10.418Scheduled task start time E20.185Mission price E30.397To sum up, it can be seen from the table that the proportion of tasks that have been completed has a greater weight in the degree of completion of the task points, and it can be clearly seen from the first-level indicators that task density, personnel density, personnel reputation value, and task price are two level indicators have a greater impact weight. To this end, combined with the modified model, the overall analysis of the completion of each task point before and after the modification of the model is carried out. The analysis chart of the completion ratio of task points is obtained, as shown in Figure2.Figure 2
The proportion of completed tasks to the total task points in the specified area.It can be seen from Figure2 that when the original scheme is implemented in a small number of areas, the task completion degree is higher than that of the modified scheme, but the revised scheme is better than the original scheme in most areas. Therefore, the implementation of the revised scheme in general is beneficial to facilitate the completion of the task.


## 4. Evaluation Model of Audit Effect Improvement Based on Grey Correlation

This paper combines the grey relational analysis to carry out the research work of the financial auditing effect and improvement evaluation. By establishing the initial evaluation system of the evaluation index and the set of improvement effect evaluation factors, we established an audit effect improvement evaluation model based on grey correlation.(9)X0′=x0′1,x0′2,...,x0′n,Xi′=xikXi¯,Xi¯=1n∑k=1nxik,k=1,2,...n,γik=Δmin+ρΔmaxΔik+ρΔmax,ρ∈0,1,k=1,2,...n;i=1,2,...n,γi=1n∑k=1nγik,i=1,2,…n.Secondary indicators such as task completion time, task completion quality, and task completion coverage are introduced to assess the new plan’s implementation effect. Primary indicators such as task price, reward amount, task volume, personnel credibility, personnel density, network density, and regional development level must be considered as connected influencing elements of secondary indicators. The secondary indicators are averaged, and a numerical list of job completion quality is generated, as shown in Table6.Table 6
Number list of task completion quality.
Task completion qualityPersonnel credibilityTask volume10.7910.8171.25720.9100.9131.14031.0751.0080.99441.1341.1030.84851.1191.1600.760Factor analysis is used in this study to extract common components from variable groupings. The correlation coefficient matrix served as the basis for the factor analysis, and principal component analysis was utilised to identify the components with an 85% cumulative contribution. Whenn principle components are retained after principal component analysis, the commonality is determined as the row square sum of the eigenvectors. And, this value is used to replace the value of the diagonal of the correlation matrix to form an approximate correlation matrix. On the basis of the approximate correlation coefficient matrix, the number of factors and the coefficients of the factors are determined by repeatedly calculating the eigenvalues and eigenvectors, and Table 7 is obtained.Table 7
Composition coefficient table.
Three major indicatorsComposition coefficientTask completion time−0.435Task completion quality0.645Task completion coverage0.526The component coefficients of the three indicators about the completion of audit tasks are. In addition, by analyzing the task quality, the audit results before and after improvement are obtained. Figure3 shows the audit results before improvement. Figure 4 shows the improved auditing effect.Figure 3
Audit results before improvement.Figure 4
Improved audit effect.The fitting findings in Figures3 and 4 show that the scheme’s implementation impact has a good fitting effect and can be utilised to evaluate the improvement effect of financial auditing. The financial industry’s relevance to national economic security has grown, and the government’s oversight of financial institutions has gotten more severe and perfect. External auditing, on the other hand, will not be able to entirely tackle the problem of information asymmetry, and the need for financial businesses’ internal control will become increasingly apparent. The research direction of financial enterprise auditing will be how to assess the internal control efficiency and internal control auditing of financial companies.


## 5. Conclusion

Many elements impact the decision-making process while making investing decisions, especially with so much data available nowadays on financial markets. In order to make the portfolio and risk management process easier, quantitative methodologies and models are continually being created. Maintaining financial security is the core content of maintaining economic security. The maintenance of financial security should be the primary goal of financial auditing. Through empirical research and analysis, this research can draw the indicators of relevant financial institutions that should be concerned about systemic risk in financial auditing.The purpose of this study was to see how GRA outcomes impact portfolio creation. The findings are comparable to the initial indifference curve built via the portfolio theory of asset allocation. Since the research on the quality of financial auditing is still in its infancy, many issues still need further research by more researchers. This paper does not subdivide financial enterprises. In the financial industry, banking, insurance, and securities industries all have their characteristics. It may be more beneficial to subdivide financial enterprises in future research. On the one hand, this paper hopes to make certain theoretical contributions to expanding the research approach and research vision of the financial audit function. On the other hand, it makes practical explorations on how to play the role of the immune system in government auditing in the financial field, to play the important responsibility of preventing financial risks and ensuring financial security, which can provide reference ideas and suggestions for the current financial auditing innovation auditing work. However, my study contains limitations that may impact the precision of the findings, and it is restricted to the level of my research, so future generations will need to improve and conduct comparable research.



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