# The Establishment of Risk Evaluation Index System for Small- and Medium-Sized Agency Bookkeeping Companies

Authors: Qingfu Wu; Xiaoqian Zhang
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

In recent years, China’s economy has developed rapidly; many small companies have risen rapidly; and the tax system has become more and more standardized. Because many small businesses cannot afford to hire full-time accountants, they opt to outsource accounting services, giving small- and medium-sized bookkeeping firms a large market space. However, these opportunities also bring huge operational risks to small- and medium-sized bookkeeping companies. The purpose of this research is to help such enterprises carry out risk management and reduce operational risks. This study uses an analytic hierarchy process and a fuzzy comprehensive assessment approach to successfully combine quantitative and qualitative analysis and create a multilevel analysis structure model of the risk management evaluation index system of small- and medium-sized agency accounting firms. The structural model is verified by a case, the specific risk score of each factor is calculated through the scores of 20 experts, and the importance of risk is judged according to the size of the score, indicating that the structural model is feasible.


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## Body

## 1. Introduction

In order to promote the healthy development of the agency bookkeeping industry, the “Administrative Measures for Agency Bookkeeping” was officially implemented in May 2016, which once again standardized the institutional management of the agency bookkeeping industry [1], but this did not fundamentally solve the problem of industrial development. The Financial Accounting (2018) No. 32 document particularly emphasized the need to strictly manage agency bookkeeping institutions, establish and improve the integrity incentive and untrustworthy punishment mechanism for the agency bookkeeping industry, and regulate the management of industry associations [2]. In March 2019, the Ministry of Finance issued relevant regulations to simplify the application materials for agency bookkeeping qualifications, shorten the statutory approval time limit, and stimulate the vitality of market entities [3]. The bookkeeping industry has experienced nearly 30 years of development, from the traditional manual mode to the computerized mode [4]. Due to the development of artificial intelligence, the accounting and taxation of agency bookkeeping companies have gradually become intelligent [5], which has brought greater influence to small- and medium-sized bookkeeping companies, and the problem of risk management has become increasingly prominent [6].


## 2. Methodology

### 2.1. Basic Method Theory

In the “Comprehensive Risk Management Framework” released by COSO in 2003, comprehensive risk management includes three dimensions [7] as shown in Figure 1.Figure 1
Comprehensive risk management framework.The basic process of comprehensive risk management is divided into five steps. The implementation of risk management is inseparable from the communication of information [8]. Therefore, a complete risk management information system must be established [9], as shown in Figure 2.Figure 2
Five steps to comprehensive risk management.The formation process of agency bookkeeping risk: risk event—risk taker—risk loss [10], as shown in Figure 3.Figure 3
Formation diagram of agency bookkeeping risk.


### 2.2. Choice of Risk Assessment Method

Risk assessment mainly refers to the qualitative or quantitative analysis of the probability and impact of risk events [11]. This research mainly adopts the analytic hierarchy process and the fuzzy comprehensive evaluation method to quantitatively analyze the risk of the agency bookkeeping company [12].


#### 2.2.1. AHP

AHP is an analysis method based on hierarchical decision-making [13]. For unstructured and relatively complex decisions [14], the use of AHP will greatly reduce the amount of engineering [15].The specific steps of AHP are as follows: (1) constructing the index system, (2) constructing the judgment matrix, (3) calculating the hierarchical weight [16], (4) checking the consistency of each layer, (5) calculating the combined weight, (6) total consistency test, and (7) determining the weight as shown in Figure 4.Figure 4
The specific step of the analytic hierarchy process.


#### 2.2.2. Fuzzy Comprehensive Evaluation Method

The fuzzy comprehensive evaluation method is a comprehensive evaluation method that transforms qualitative evaluation into quantitative evaluation through the membership degree theory of fuzzy mathematics [17].The specific steps of the fuzzy comprehensive evaluation method are [18]: (1) determining the evaluation object, (2) establishing the index system, (3) determining the evaluation set, (4) determining the index weight, (5) fuzzy comprehensive evaluation, and (6) analysis of the evaluation results as shown in Figure 5.Figure 5
The specific step of the fuzzy comprehensive evaluation method.


## 2.1. Basic Method Theory

In the “Comprehensive Risk Management Framework” released by COSO in 2003, comprehensive risk management includes three dimensions [7] as shown in Figure 1.Figure 1
Comprehensive risk management framework.The basic process of comprehensive risk management is divided into five steps. The implementation of risk management is inseparable from the communication of information [8]. Therefore, a complete risk management information system must be established [9], as shown in Figure 2.Figure 2
Five steps to comprehensive risk management.The formation process of agency bookkeeping risk: risk event—risk taker—risk loss [10], as shown in Figure 3.Figure 3
Formation diagram of agency bookkeeping risk.


## 2.2. Choice of Risk Assessment Method

Risk assessment mainly refers to the qualitative or quantitative analysis of the probability and impact of risk events [11]. This research mainly adopts the analytic hierarchy process and the fuzzy comprehensive evaluation method to quantitatively analyze the risk of the agency bookkeeping company [12].


### 2.2.1. AHP

AHP is an analysis method based on hierarchical decision-making [13]. For unstructured and relatively complex decisions [14], the use of AHP will greatly reduce the amount of engineering [15].The specific steps of AHP are as follows: (1) constructing the index system, (2) constructing the judgment matrix, (3) calculating the hierarchical weight [16], (4) checking the consistency of each layer, (5) calculating the combined weight, (6) total consistency test, and (7) determining the weight as shown in Figure 4.Figure 4
The specific step of the analytic hierarchy process.


### 2.2.2. Fuzzy Comprehensive Evaluation Method

The fuzzy comprehensive evaluation method is a comprehensive evaluation method that transforms qualitative evaluation into quantitative evaluation through the membership degree theory of fuzzy mathematics [17].The specific steps of the fuzzy comprehensive evaluation method are [18]: (1) determining the evaluation object, (2) establishing the index system, (3) determining the evaluation set, (4) determining the index weight, (5) fuzzy comprehensive evaluation, and (6) analysis of the evaluation results as shown in Figure 5.Figure 5
The specific step of the fuzzy comprehensive evaluation method.


## 2.2.1. AHP

AHP is an analysis method based on hierarchical decision-making [13]. For unstructured and relatively complex decisions [14], the use of AHP will greatly reduce the amount of engineering [15].The specific steps of AHP are as follows: (1) constructing the index system, (2) constructing the judgment matrix, (3) calculating the hierarchical weight [16], (4) checking the consistency of each layer, (5) calculating the combined weight, (6) total consistency test, and (7) determining the weight as shown in Figure 4.Figure 4
The specific step of the analytic hierarchy process.


## 2.2.2. Fuzzy Comprehensive Evaluation Method

The fuzzy comprehensive evaluation method is a comprehensive evaluation method that transforms qualitative evaluation into quantitative evaluation through the membership degree theory of fuzzy mathematics [17].The specific steps of the fuzzy comprehensive evaluation method are [18]: (1) determining the evaluation object, (2) establishing the index system, (3) determining the evaluation set, (4) determining the index weight, (5) fuzzy comprehensive evaluation, and (6) analysis of the evaluation results as shown in Figure 5.Figure 5
The specific step of the fuzzy comprehensive evaluation method.


## 3. Establishment of the Risk Evaluation Index System for Small- and Medium-Sized Agency Bookkeeping Companies

### 3.1. Establishment of the Risk Assessment Index System

In practical applications, there are many types of risk factor identification methods [19], mainly including the following: (1) brainstorming method, (2) analysis process method [20], (3) analysis of relevant scenarios, (4) risk decomposition method [21], and (5) editing event tree method [22]. According to the actual situation of small- and medium-sized agency bookkeeping companies, this paper adopts the brainstorming method to identify the risk factors of these companies.Organized and sent 20 experts to conduct in-depth research on small- and medium-sized bookkeeping companies. Through the discussion, summarize the main risks in five aspects: policy and legal risk, industry competition risk, information technology risk, undertaking business risk, and practitioner risk [23]. In the case of ensuring the comprehensiveness of the risk evaluation system, the risk evaluation index system in Table 1 is summarized and determined [24].Table 1
Risk evaluation index system.
Target layerCriterion layerIndicator layerRisk assessment influencing factors A of small- and medium-sized bookkeeping companiesPolicy and legal risk A1Industry policy risk a11Legal and regulatory risks a12Industry regulatory risk a13Industry competition risk A2Risk a21 of low-price competition among peersInfiltrator substitution risk a22Service homogenization risk a23Information technology risk A3Financial software technology risk a31Financial data access risk a32Internal information process risk a33Undertaking business risk A4Delegator moral hazard a41Risk a42 of loss of customer dataAccounting information distortion risk a43Service charge recovery risk a44Practitioner risk A5Professional skills risk a51Professional ethics hazard a52Employee training risk a53Liquidity risk a54


### 3.2. Establishment of Risk Assessment Set

In order to make the evaluation effect clearer, the evaluation using gradients within a range of the evaluated risk factors is usually adopted [25]. Five different continuous grade categories are selected for the agency bookkeeping risk evaluation set, and the five evaluation results are “no risk,” “small risk,” “average risk,” “high risk,” and “huge risk,” Specifically, it is represented by V = {V1, V2, V3, V4, V5}, in which the five evaluation results are, respectively, corresponding to the scores of “20,” “40,” “60,” “80,” and “100.” Higher scores indicate greater risk, as shown in Table 2.Table 2
Risk assessment level.
Risk levelEvaluation resultsEvaluation scores1No risk202Small risk403Average risk604High risk805Huge risk100


### 3.3. Establishment of Risk Indicator Weights

#### 3.3.1. Establishing the Judgment Matrix

Use an appropriate scale to construct a judgment matrix by comparison [26] and establish a comparative judgment matrix A for the risk indicators after statistical analysis:(1)A=ajin×n=a11a12⋯a1na21a22⋯a2n⋮⋮⋮am1am2⋯amn.


#### 3.3.2. Calculation of Criterion Layer Weights

The calculation of the weight of the criterion layer can be divided into three steps: one is to normalize the risk judgment matrix A of the criterion layer of the company to obtain a new matrix [27]. The weights are obtained by normalization [28]. The third is the matrix consistency test [29].(1)
Normalize each column of the A matrix to obtain a new matrixZ:(2)Zij=Aij∑Aij.(2)
The eigenvectors are obtained by summing each row of the matrix, and then the weights are obtained by normalizing the eigenvectors:(3)Wi=Zi∑Aij.WA = (WA 1, WA 2, WA 3, WA 4, WA 5).From this, it can be concluded that WA1 to WA5 are the weight ratios of each risk factor index in each criterion layer, and the next work is to take a consistency check on the weight of each index obtained.(3)
Matrix consistency testWe calculate the largest eigenroot as follows:(4)λmax=∑AWinWi.where λmax represents the largest eigenvalue, A represents the corresponding matrix, W represents the eigenvector, and i represents the corresponding element in the matrix. The CI scale is determined based on the characteristic root. The formula is as follows:We calculate the consistency index of the judgment matrix as follows:(5)CI=λmax−nn−1.Factor CR agreement was calculated according to the RI corresponding to the CI. In fact, RI is a constant, which represents the average random consistency index. According to the order of the matrix, the ratio of the matrix consistency index CI and the average random consistency index RI of the same order can be queried in the table, which is called the random consistency ratio. If the condition of CR < 0.10 is satisfied, it can indicate that the judgment matrix has passed the consistency check, and if it is not satisfied, it means that the consistency check has not passed [30].We calculate the random consistency ratio as follows:(6)CR=CIRI.


#### 3.3.3. Calculation of Index Layer Weights and Comprehensive Weights

When determining other weights, you can also collect and analyze data and use the same method as above to calculate the standard layer judgment matrix weight.According to the formula: the comprehensive weight of the indicator layer = the weight of the indicator layer × the weight of the criterion layer, the comprehensive weight of each indicator of the company’s indicator layer can be obtained by calculation.


### 3.4. Application of the Fuzzy Comprehensive Evaluation Method

After the weight of each risk factor index is obtained, the membership degree of the fuzzy comprehensive evaluation set should be calculated next, and the fuzzy comprehensive evaluation should be implemented by combining the weight and the membership degree [31]. The determination of membership degree is highly subjective, requiring each evaluation expert to be careful [32]. The membership matrix function usually refers to a new matrix that is synthesized after the evaluation indicators of all matrices are rated by membership [33], as shown in the following formula:(7)R=r11⋯r1n⋮⋱⋮rm1⋯amn.R can be regarded as a mapping of the matrix membership evaluation set, and the membership degree is treated as a condition of fuzzy operation, and the fuzzy evaluation result can be obtained by multiplying it by the weight. The specific calculation formula is shown in the following formula:(8)B=W·R=W1,W2,W3,…,Wn·r11⋯rln⋮⋱⋮rm1⋯rmn.Formula (8) can be used to calculate the fuzzy comprehensive evaluation score of the five matrices of the criterion layer “A1” to “A5.” From the above calculation ideas, usually use “very important, relatively important, generally important, less important, very unimportant,” the 5-level satisfaction evaluation level that makes a reasonable evaluation of all evaluation indicators, so as to obtain the membership degree. Twenty experts selected Appendix B and obtained the evaluation frequency table after statistics. The corresponding membership degree matrix can be obtained by obtaining the membership degree of each index.


## 3.1. Establishment of the Risk Assessment Index System

In practical applications, there are many types of risk factor identification methods [19], mainly including the following: (1) brainstorming method, (2) analysis process method [20], (3) analysis of relevant scenarios, (4) risk decomposition method [21], and (5) editing event tree method [22]. According to the actual situation of small- and medium-sized agency bookkeeping companies, this paper adopts the brainstorming method to identify the risk factors of these companies.Organized and sent 20 experts to conduct in-depth research on small- and medium-sized bookkeeping companies. Through the discussion, summarize the main risks in five aspects: policy and legal risk, industry competition risk, information technology risk, undertaking business risk, and practitioner risk [23]. In the case of ensuring the comprehensiveness of the risk evaluation system, the risk evaluation index system in Table 1 is summarized and determined [24].Table 1
Risk evaluation index system.
Target layerCriterion layerIndicator layerRisk assessment influencing factors A of small- and medium-sized bookkeeping companiesPolicy and legal risk A1Industry policy risk a11Legal and regulatory risks a12Industry regulatory risk a13Industry competition risk A2Risk a21 of low-price competition among peersInfiltrator substitution risk a22Service homogenization risk a23Information technology risk A3Financial software technology risk a31Financial data access risk a32Internal information process risk a33Undertaking business risk A4Delegator moral hazard a41Risk a42 of loss of customer dataAccounting information distortion risk a43Service charge recovery risk a44Practitioner risk A5Professional skills risk a51Professional ethics hazard a52Employee training risk a53Liquidity risk a54


## 3.2. Establishment of Risk Assessment Set

In order to make the evaluation effect clearer, the evaluation using gradients within a range of the evaluated risk factors is usually adopted [25]. Five different continuous grade categories are selected for the agency bookkeeping risk evaluation set, and the five evaluation results are “no risk,” “small risk,” “average risk,” “high risk,” and “huge risk,” Specifically, it is represented by V = {V1, V2, V3, V4, V5}, in which the five evaluation results are, respectively, corresponding to the scores of “20,” “40,” “60,” “80,” and “100.” Higher scores indicate greater risk, as shown in Table 2.Table 2
Risk assessment level.
Risk levelEvaluation resultsEvaluation scores1No risk202Small risk403Average risk604High risk805Huge risk100


## 3.3. Establishment of Risk Indicator Weights

### 3.3.1. Establishing the Judgment Matrix

Use an appropriate scale to construct a judgment matrix by comparison [26] and establish a comparative judgment matrix A for the risk indicators after statistical analysis:(1)A=ajin×n=a11a12⋯a1na21a22⋯a2n⋮⋮⋮am1am2⋯amn.


### 3.3.2. Calculation of Criterion Layer Weights

The calculation of the weight of the criterion layer can be divided into three steps: one is to normalize the risk judgment matrix A of the criterion layer of the company to obtain a new matrix [27]. The weights are obtained by normalization [28]. The third is the matrix consistency test [29].(1)
Normalize each column of the A matrix to obtain a new matrixZ:(2)Zij=Aij∑Aij.(2)
The eigenvectors are obtained by summing each row of the matrix, and then the weights are obtained by normalizing the eigenvectors:(3)Wi=Zi∑Aij.WA = (WA 1, WA 2, WA 3, WA 4, WA 5).From this, it can be concluded that WA1 to WA5 are the weight ratios of each risk factor index in each criterion layer, and the next work is to take a consistency check on the weight of each index obtained.(3)
Matrix consistency testWe calculate the largest eigenroot as follows:(4)λmax=∑AWinWi.where λmax represents the largest eigenvalue, A represents the corresponding matrix, W represents the eigenvector, and i represents the corresponding element in the matrix. The CI scale is determined based on the characteristic root. The formula is as follows:We calculate the consistency index of the judgment matrix as follows:(5)CI=λmax−nn−1.Factor CR agreement was calculated according to the RI corresponding to the CI. In fact, RI is a constant, which represents the average random consistency index. According to the order of the matrix, the ratio of the matrix consistency index CI and the average random consistency index RI of the same order can be queried in the table, which is called the random consistency ratio. If the condition of CR < 0.10 is satisfied, it can indicate that the judgment matrix has passed the consistency check, and if it is not satisfied, it means that the consistency check has not passed [30].We calculate the random consistency ratio as follows:(6)CR=CIRI.


### 3.3.3. Calculation of Index Layer Weights and Comprehensive Weights

When determining other weights, you can also collect and analyze data and use the same method as above to calculate the standard layer judgment matrix weight.According to the formula: the comprehensive weight of the indicator layer = the weight of the indicator layer × the weight of the criterion layer, the comprehensive weight of each indicator of the company’s indicator layer can be obtained by calculation.


## 3.3.1. Establishing the Judgment Matrix

Use an appropriate scale to construct a judgment matrix by comparison [26] and establish a comparative judgment matrix A for the risk indicators after statistical analysis:(1)A=ajin×n=a11a12⋯a1na21a22⋯a2n⋮⋮⋮am1am2⋯amn.


## 3.3.2. Calculation of Criterion Layer Weights

The calculation of the weight of the criterion layer can be divided into three steps: one is to normalize the risk judgment matrix A of the criterion layer of the company to obtain a new matrix [27]. The weights are obtained by normalization [28]. The third is the matrix consistency test [29].(1)
Normalize each column of the A matrix to obtain a new matrixZ:(2)Zij=Aij∑Aij.(2)
The eigenvectors are obtained by summing each row of the matrix, and then the weights are obtained by normalizing the eigenvectors:(3)Wi=Zi∑Aij.WA = (WA 1, WA 2, WA 3, WA 4, WA 5).From this, it can be concluded that WA1 to WA5 are the weight ratios of each risk factor index in each criterion layer, and the next work is to take a consistency check on the weight of each index obtained.(3)
Matrix consistency testWe calculate the largest eigenroot as follows:(4)λmax=∑AWinWi.where λmax represents the largest eigenvalue, A represents the corresponding matrix, W represents the eigenvector, and i represents the corresponding element in the matrix. The CI scale is determined based on the characteristic root. The formula is as follows:We calculate the consistency index of the judgment matrix as follows:(5)CI=λmax−nn−1.Factor CR agreement was calculated according to the RI corresponding to the CI. In fact, RI is a constant, which represents the average random consistency index. According to the order of the matrix, the ratio of the matrix consistency index CI and the average random consistency index RI of the same order can be queried in the table, which is called the random consistency ratio. If the condition of CR < 0.10 is satisfied, it can indicate that the judgment matrix has passed the consistency check, and if it is not satisfied, it means that the consistency check has not passed [30].We calculate the random consistency ratio as follows:(6)CR=CIRI.


## 3.3.3. Calculation of Index Layer Weights and Comprehensive Weights

When determining other weights, you can also collect and analyze data and use the same method as above to calculate the standard layer judgment matrix weight.According to the formula: the comprehensive weight of the indicator layer = the weight of the indicator layer × the weight of the criterion layer, the comprehensive weight of each indicator of the company’s indicator layer can be obtained by calculation.


## 3.4. Application of the Fuzzy Comprehensive Evaluation Method

After the weight of each risk factor index is obtained, the membership degree of the fuzzy comprehensive evaluation set should be calculated next, and the fuzzy comprehensive evaluation should be implemented by combining the weight and the membership degree [31]. The determination of membership degree is highly subjective, requiring each evaluation expert to be careful [32]. The membership matrix function usually refers to a new matrix that is synthesized after the evaluation indicators of all matrices are rated by membership [33], as shown in the following formula:(7)R=r11⋯r1n⋮⋱⋮rm1⋯amn.R can be regarded as a mapping of the matrix membership evaluation set, and the membership degree is treated as a condition of fuzzy operation, and the fuzzy evaluation result can be obtained by multiplying it by the weight. The specific calculation formula is shown in the following formula:(8)B=W·R=W1,W2,W3,…,Wn·r11⋯rln⋮⋱⋮rm1⋯rmn.Formula (8) can be used to calculate the fuzzy comprehensive evaluation score of the five matrices of the criterion layer “A1” to “A5.” From the above calculation ideas, usually use “very important, relatively important, generally important, less important, very unimportant,” the 5-level satisfaction evaluation level that makes a reasonable evaluation of all evaluation indicators, so as to obtain the membership degree. Twenty experts selected Appendix B and obtained the evaluation frequency table after statistics. The corresponding membership degree matrix can be obtained by obtaining the membership degree of each index.


## 4. Case Validation

### 4.1. Case Situation

HIG bookkeeping company was established in 2013. It is a typical small- and medium-sized bookkeeping company in China. The company has a registered capital of 1 million yuan. Its business scope includes accounting business consulting services, accounting consultants, agency bookkeeping services [34], agency financial and tax reporting services, agent for industrial and commercial registration, enterprise annual report service, agent for various licenses, and agent for trademark registration and patent application [35].After the discussion of 20 experts, the final conclusion is drawn to the HIG company’s agency bookkeeping risk formation table, as shown in Table3.Table 3
Risk formation table of HIG’s agency bookkeeping.
Risk factorPossible risk eventsRisk takerRisk lossPolicy and legal risksInadequate state support for the industryHIG companyLoss of business developmentContractual disputeHIG companyLoss of business managementIrregularities in the industryHIG companyLoss of business developmentIndustry competition riskIndustry price disorderHIG companyLoss of business developmentMarket share is seized by newcomersHIG companyLoss of business developmentNo competitive advantageHIG companyLoss of business developmentInformation technology riskIntelligent financial softwareHIG companyLoss of business developmentLoss of financial dataHIG companyLoss of service qualityPoor communication of internal informationHIG companyLoss of business managementUndertaking business riskPrincipal’s tax evasionHIG companyLoss of business managementLoss of customer dataHIG company, Entrusting companyLoss of service qualityDistortion of accounting informationHIG company, Entrusting companyLoss of service qualityNot received service feeHIG companyLoss of business managementPractitioner riskUnprofessional staffHIG companyLoss of service qualityThe moral quality of the employees is not high, and they make false accountsHIG companyLoss of service qualityEmployee training is not appropriate, or if they learn skills, they will leaveHIG companyLoss of labor costsResign after being familiar with the operation process, revealing business opportunitiesHIG companyLoss of business talent


### 4.2. Establishment of Risk Factor Indicator Weights

#### 4.2.1. Constructing the Judgment Matrix

A total of 20 experts were invited for this case, including 3 managers and deputy managers of the company; one person in charge of each department of Administration Department, Operation Department, Business Department, and Finance Department; and 13 external financial experts. After statistical analysis, a comparison (judgment) matrix A is established for the risk indicators:(9)A=ajin×n=a11a12⋯a1na21a22⋯a2n⋮⋮⋮am1am2⋯amn,A=14123131411413142413121331311534251.


#### 4.2.2. Calculation of Criterion Layer Weights

(1)
Normalize each column of theA matrix to obtain a new matrix Z as follows:(10)Zij=Aij∑Aij,Z=0.150.250.120.240.150.040.060.060.030.110.300.250.240.240.220.050.190.080.080.090.460.250.490.410.44.(2)
The eigenvectors are obtained by summing each row of the matrix, and then the weights are obtained by normalizing the eigenvectors [36]:(11)Wi=Zi∑Aij.WA = (WA 1, WA 2, WA 3, WA 4, WA 5) = (0.1827, 0.0596, 0.2522, 0.0977, 0.4078).(3)
Matrix consistency testWe calculate the largest eigenroot as follows:(12)λmax=∑AWinWi.Here, λmax = 5.2541.We calculate the consistency index of the judgment matrix as follows:(13)CI=λmax−nn−1.Here, CI = 0.0635.The average random consistency index is shown in Table4.Table 4
Mean random consistency indicator.
Order,n123456789RI000.520.891.121.261.361.411.46We calculate the random consistency ratio as follows:(14)CR=CIRI.H CR = 0.0567 < 0.10.Therefore, it can be determined that WA = (0.1827, 0.0596, 0.2522, 0.0977, 0.4078) is the criterion layer weight that satisfies the consistency test conditions.


#### 4.2.3. Calculation of Indicator Layer Weights

Using the same method as above, the standard layer judgment matrix weights are calculated as shown in Tables5–9, respectively.Table 5
The scoring results of the policy and legal risk indicator layer.
Policy and legal risk A1Industry policy risk a11Legal and regulatory risks a12Industry regulatory risk a13WiIndustry policy risk a1111/21/30.1717Legal and regulatory risks a12213/20.4414Industry regulatory risk a1332/310.3869Table 6
The scoring results of the industry competition risk index layer.
Industry competition risk A2Risk a21 of low-price competition among peersInfiltrator substitution risk a22Service homogenization risk a23WiRisk a21 of low-price competition among peers11/41/50.0994Infiltrator substitution risk a22412/30.3736Service homogenization risk a2353/210.5270Table 7
The scoring results of the information technology risk index layer.
Information technology risk A3Financial software technology risk a31Financial data access risk a32Internal information process risk a33WiFinancial software technology risk a311430.6300Financial data access risk a321/412/30.1515Internal information process risk a331/33/210.2185Table 8
The scoring results of the indicator layer for undertaking business risks.
Undertaking business risk A4Delegator moral hazard a41Risk a42 of loss of customer dataAccounting information distortion risk a43Service charge recovery risk a44WiDelegator moral hazard a41131/330.2664Risk a42 of loss of customer data1/311/51/20.0840Accounting information distortion risk a4335130.5083Service charge recovery risk a441/321/310.1413Table 9
Scoring results at the practitioner risk indicator layer.
Practitioner risk A5Professional skills risk a51Professional ethics hazard a52Employee training risk a53Liquidity risk a54WiProfessional skills risk a5113450.5325Professional ethics hazard a521/31330.2542Employee training risk a531/41/311/20.0911Liquidity risk a541/51/3210.1222λmax = 3.0735 and CR = 0.0707 < 0.10.Indicator layer weights for policy legal risks: WA1 = (0.1717, 0.4414, 0.3869).λmax = 3.0037 and CR = 0.0036 < 0.10.The indicator layer weight of industry competition risk: WA2 = (0.0994, 0.3736, 0.5270).λmax = 3.0015 and CR = 0.0014 < 0.10.Indicator layer weights for information technology risk: WA3 = (0.6300, 0.1515, 0.2185).λmax = 4.1315 and CR = 0.0493 < 0.10.Indicator layer weights for undertaking business risks: WA4 = (0.2664, 0.0840, 0.5083, 0.1413).λmax = 4.1471 and CR = 0.0551 < 0.10.The weight of the practitioner risk indicator layer: WA5 = (0.5325, 0.2542, 0.0911, 0.1222).


#### 4.2.4. Calculation of Comprehensive Weight of Index Layer

According to the formula: the comprehensive weight of the indicator layer = the weight of the indicator layer × the weight of the criterion layer, the comprehensive weight of each indicator in the indicator layer of HIG can be obtained by calculation, as shown in Table10.Table 10
The comprehensive weight of the indicators of the HIG company’s indicator layer.
IndexPolicy and legal risk A1Industry competition risk A2Information technology risk A3Undertaking business risk A4Practitioner risk A5The comprehensive weight of the indicator layerRank the top three0.18270.05960.25220.09770.4078Industry policy risk a110.17170.0314Legal and regulatory risks a120.44140.0806Industry regulatory risk a130.38690.0707Risk a21 of low-price competition among peers0.09940.0059Infiltrator substitution risk a220.37360.0223Service homogenization risk a230.52700.0314Financial software technology risk a310.63000.15892Financial data access risk a320.15150.0382Internal information process risk a330.21850.0551Delegator moral hazard a410.26640.0260Risk a42 of loss of customer data0.08400.0082Accounting information distortion risk a430.50830.0497Service charge recovery risk a440.14130.0138Professional skills risk a510.53250.21711Professional ethics hazard a520.25420.10373Employee training risk a530.09110.0371Liquidity risk a540.12220.0498It can be found from Table10 that the top three comprehensive weights of the indicator layer are professional skills risk, financial software technology risk, and professional ethics risk.


### 4.3. Application of the Fuzzy Comprehensive Evaluation Method

#### 4.3.1. Establishment of the Membership Matrix

Twenty experts selected Appendix B and obtained the evaluation frequency table after statistics, as shown in Table11.Table 11
Statistical table of frequency of satisfaction evaluation of five levels of risk factors.
Risk factorVery importantRelatively importantGenerally importantLess importantVery unimportantFrequencyFrequencyFrequencyFrequencyFrequencyPolicy and legal risk A146820Industry policy risk a1128820Legal and regulatory risks a1248620Industry regulatory risk a1326840Industry competition risk A226840Risk a21 of low-price competition among peers241022Infiltrator substitution risk a22061022Service homogenization risk a23221042Information technology risk A346820Financial software technology risk a3166422Financial data access risk a3228640Internal information process risk a3326840Undertaking business risk A444840Delegator moral hazard a4106842Risk a42 of loss of customer data26822Accounting information distortion risk a4328840Service charge recovery risk a4406842Practitioner risk A5261020Professional skills risk a5128820Professional ethics hazard a5226840Employee training risk a53061040Liquidity risk a54241022Taking the membership evaluation of a11 as an example, it is very important for 2 experts to choose a11; the choice of 8 experts is more important; the choice of 8 experts is generally important; the choice of 2 experts is not very important; and the choice of no experts is very unimportant. Then the membership degree of a11 is as follows: r11 = (0.1, 0.4, 0.4, 0.1, 0), and so on, the corresponding membership degree matrix can be obtained by obtaining the membership degree of each index.(15)R1=0.10.40.40.100.20.40.30.100.10.30.40.20,R2=0.10.20.50.10.100.30.50.10.10.10.10.50.20.1,R3=00.30.20.10.10.10.40.30.200.10.30.40.20,R4=00.30.40.20.10.10.30.40.10.10.10.40.40.2000.30.40.20.1,R5=0.10.40.40.100.10.30.40.2000.30.50.200.10.20.50.10.1,R=0.20.30.40.100.10.30.40.200.20.30.40.100.20.20.40.200.10.30.50.10.


#### 4.3.2. Fuzzy Operations

Taking the criterion-level indicator of policy and legal risk as an example, according to formula (8), its membership algorithm is(16)B=W1·R1=0.1717,0.4414,0.3569·0.10.40.40.100.20.40.30.100.10.30.40.20.B1 = (0.1411, 0.3523, 0.3439, 0.1327, 0)The same can be obtained:B2 = (0.0626, 0.1847, 0.5, 0.1527, 0.1)B3 = (0.226, 0.3151, 0.2589, 0.137, 0.063)B4 = (0.0592, 0.3508, 0.4, 0.1916, 0.0492)B5 = (0.0909, 0.341, 0.4213, 0.1345, 0.0122)Normalized to get:B1 = (0.1455, 0.3632, 0.3545, 0.1368, 0)B2 = (0.0626, 0.1847, 0.5, 0.1527, 0.1)B3 = (0.226, 0.3151, 0.2589, 0.137, 0.063)B4 = (0.0563, 0.3338, 0.3807, 0.1823, 0.0468)B5 = (0.0909, 0.341, 0.4213, 0.1345, 0.0122)Target layer fuzzy evaluation results:B = W·R = (0.1533, 0.2902, 0.4408, 0.1157, 0)Using the corresponding scores of the previous evaluation set, the risk scores of each factor can be obtained by operation:B1 = 0.1455 × 20 + 0.3632 × 40 + 0.3545 × 60 + 0.1368 ×  80 = 49.65B2 = 0.0626 × 20 + 0.1847 × 40 + 0.5 × 60 + 0.1527 ×  80 + 0.1 × 100 = 60.86B3 = 0.226 × 20 + 0.3151 × 40 + 0.2589 × 60 + 0.137 ×  80 + 0.063 × 100 = 49.92B4 = 0.0563 × 20 + 0.3338 × 40 + 0.3807 × 60 +  0.1823 × 80 + 0.0468 × 100 = 56.58B5 = 0.0909 × 20 + 0.341 × 40 + 0.4213 × 60 + 0.1345 ×  80 + 0.0122 × 100 = 52.72B = 0.1533 × 20 + 0.2902 × 40 + 0.4408 × 60 + 0.1157 ×  80 = 50.38


### 4.4. Analysis of Risk Assessment Results

From the results of the fuzzy comprehensive evaluation, the influence of each risk factor in the criterion layer can be comprehensively analyzed; the degree of attention to the risk factors can be determined; and corresponding countermeasures can be formulated. Finally, analyze the main risk factors, focus on the top three risk factors ranked by the comprehensive weight of the indicator layer, and focus on the response.


## 4.1. Case Situation

HIG bookkeeping company was established in 2013. It is a typical small- and medium-sized bookkeeping company in China. The company has a registered capital of 1 million yuan. Its business scope includes accounting business consulting services, accounting consultants, agency bookkeeping services [34], agency financial and tax reporting services, agent for industrial and commercial registration, enterprise annual report service, agent for various licenses, and agent for trademark registration and patent application [35].After the discussion of 20 experts, the final conclusion is drawn to the HIG company’s agency bookkeeping risk formation table, as shown in Table3.Table 3
Risk formation table of HIG’s agency bookkeeping.
Risk factorPossible risk eventsRisk takerRisk lossPolicy and legal risksInadequate state support for the industryHIG companyLoss of business developmentContractual disputeHIG companyLoss of business managementIrregularities in the industryHIG companyLoss of business developmentIndustry competition riskIndustry price disorderHIG companyLoss of business developmentMarket share is seized by newcomersHIG companyLoss of business developmentNo competitive advantageHIG companyLoss of business developmentInformation technology riskIntelligent financial softwareHIG companyLoss of business developmentLoss of financial dataHIG companyLoss of service qualityPoor communication of internal informationHIG companyLoss of business managementUndertaking business riskPrincipal’s tax evasionHIG companyLoss of business managementLoss of customer dataHIG company, Entrusting companyLoss of service qualityDistortion of accounting informationHIG company, Entrusting companyLoss of service qualityNot received service feeHIG companyLoss of business managementPractitioner riskUnprofessional staffHIG companyLoss of service qualityThe moral quality of the employees is not high, and they make false accountsHIG companyLoss of service qualityEmployee training is not appropriate, or if they learn skills, they will leaveHIG companyLoss of labor costsResign after being familiar with the operation process, revealing business opportunitiesHIG companyLoss of business talent


## 4.2. Establishment of Risk Factor Indicator Weights

### 4.2.1. Constructing the Judgment Matrix

A total of 20 experts were invited for this case, including 3 managers and deputy managers of the company; one person in charge of each department of Administration Department, Operation Department, Business Department, and Finance Department; and 13 external financial experts. After statistical analysis, a comparison (judgment) matrix A is established for the risk indicators:(9)A=ajin×n=a11a12⋯a1na21a22⋯a2n⋮⋮⋮am1am2⋯amn,A=14123131411413142413121331311534251.


### 4.2.2. Calculation of Criterion Layer Weights

(1)
Normalize each column of theA matrix to obtain a new matrix Z as follows:(10)Zij=Aij∑Aij,Z=0.150.250.120.240.150.040.060.060.030.110.300.250.240.240.220.050.190.080.080.090.460.250.490.410.44.(2)
The eigenvectors are obtained by summing each row of the matrix, and then the weights are obtained by normalizing the eigenvectors [36]:(11)Wi=Zi∑Aij.WA = (WA 1, WA 2, WA 3, WA 4, WA 5) = (0.1827, 0.0596, 0.2522, 0.0977, 0.4078).(3)
Matrix consistency testWe calculate the largest eigenroot as follows:(12)λmax=∑AWinWi.Here, λmax = 5.2541.We calculate the consistency index of the judgment matrix as follows:(13)CI=λmax−nn−1.Here, CI = 0.0635.The average random consistency index is shown in Table4.Table 4
Mean random consistency indicator.
Order,n123456789RI000.520.891.121.261.361.411.46We calculate the random consistency ratio as follows:(14)CR=CIRI.H CR = 0.0567 < 0.10.Therefore, it can be determined that WA = (0.1827, 0.0596, 0.2522, 0.0977, 0.4078) is the criterion layer weight that satisfies the consistency test conditions.


### 4.2.3. Calculation of Indicator Layer Weights

Using the same method as above, the standard layer judgment matrix weights are calculated as shown in Tables5–9, respectively.Table 5
The scoring results of the policy and legal risk indicator layer.
Policy and legal risk A1Industry policy risk a11Legal and regulatory risks a12Industry regulatory risk a13WiIndustry policy risk a1111/21/30.1717Legal and regulatory risks a12213/20.4414Industry regulatory risk a1332/310.3869Table 6
The scoring results of the industry competition risk index layer.
Industry competition risk A2Risk a21 of low-price competition among peersInfiltrator substitution risk a22Service homogenization risk a23WiRisk a21 of low-price competition among peers11/41/50.0994Infiltrator substitution risk a22412/30.3736Service homogenization risk a2353/210.5270Table 7
The scoring results of the information technology risk index layer.
Information technology risk A3Financial software technology risk a31Financial data access risk a32Internal information process risk a33WiFinancial software technology risk a311430.6300Financial data access risk a321/412/30.1515Internal information process risk a331/33/210.2185Table 8
The scoring results of the indicator layer for undertaking business risks.
Undertaking business risk A4Delegator moral hazard a41Risk a42 of loss of customer dataAccounting information distortion risk a43Service charge recovery risk a44WiDelegator moral hazard a41131/330.2664Risk a42 of loss of customer data1/311/51/20.0840Accounting information distortion risk a4335130.5083Service charge recovery risk a441/321/310.1413Table 9
Scoring results at the practitioner risk indicator layer.
Practitioner risk A5Professional skills risk a51Professional ethics hazard a52Employee training risk a53Liquidity risk a54WiProfessional skills risk a5113450.5325Professional ethics hazard a521/31330.2542Employee training risk a531/41/311/20.0911Liquidity risk a541/51/3210.1222λmax = 3.0735 and CR = 0.0707 < 0.10.Indicator layer weights for policy legal risks: WA1 = (0.1717, 0.4414, 0.3869).λmax = 3.0037 and CR = 0.0036 < 0.10.The indicator layer weight of industry competition risk: WA2 = (0.0994, 0.3736, 0.5270).λmax = 3.0015 and CR = 0.0014 < 0.10.Indicator layer weights for information technology risk: WA3 = (0.6300, 0.1515, 0.2185).λmax = 4.1315 and CR = 0.0493 < 0.10.Indicator layer weights for undertaking business risks: WA4 = (0.2664, 0.0840, 0.5083, 0.1413).λmax = 4.1471 and CR = 0.0551 < 0.10.The weight of the practitioner risk indicator layer: WA5 = (0.5325, 0.2542, 0.0911, 0.1222).


### 4.2.4. Calculation of Comprehensive Weight of Index Layer

According to the formula: the comprehensive weight of the indicator layer = the weight of the indicator layer × the weight of the criterion layer, the comprehensive weight of each indicator in the indicator layer of HIG can be obtained by calculation, as shown in Table10.Table 10
The comprehensive weight of the indicators of the HIG company’s indicator layer.
IndexPolicy and legal risk A1Industry competition risk A2Information technology risk A3Undertaking business risk A4Practitioner risk A5The comprehensive weight of the indicator layerRank the top three0.18270.05960.25220.09770.4078Industry policy risk a110.17170.0314Legal and regulatory risks a120.44140.0806Industry regulatory risk a130.38690.0707Risk a21 of low-price competition among peers0.09940.0059Infiltrator substitution risk a220.37360.0223Service homogenization risk a230.52700.0314Financial software technology risk a310.63000.15892Financial data access risk a320.15150.0382Internal information process risk a330.21850.0551Delegator moral hazard a410.26640.0260Risk a42 of loss of customer data0.08400.0082Accounting information distortion risk a430.50830.0497Service charge recovery risk a440.14130.0138Professional skills risk a510.53250.21711Professional ethics hazard a520.25420.10373Employee training risk a530.09110.0371Liquidity risk a540.12220.0498It can be found from Table10 that the top three comprehensive weights of the indicator layer are professional skills risk, financial software technology risk, and professional ethics risk.


## 4.2.1. Constructing the Judgment Matrix

A total of 20 experts were invited for this case, including 3 managers and deputy managers of the company; one person in charge of each department of Administration Department, Operation Department, Business Department, and Finance Department; and 13 external financial experts. After statistical analysis, a comparison (judgment) matrix A is established for the risk indicators:(9)A=ajin×n=a11a12⋯a1na21a22⋯a2n⋮⋮⋮am1am2⋯amn,A=14123131411413142413121331311534251.


## 4.2.2. Calculation of Criterion Layer Weights

(1)
Normalize each column of theA matrix to obtain a new matrix Z as follows:(10)Zij=Aij∑Aij,Z=0.150.250.120.240.150.040.060.060.030.110.300.250.240.240.220.050.190.080.080.090.460.250.490.410.44.(2)
The eigenvectors are obtained by summing each row of the matrix, and then the weights are obtained by normalizing the eigenvectors [36]:(11)Wi=Zi∑Aij.WA = (WA 1, WA 2, WA 3, WA 4, WA 5) = (0.1827, 0.0596, 0.2522, 0.0977, 0.4078).(3)
Matrix consistency testWe calculate the largest eigenroot as follows:(12)λmax=∑AWinWi.Here, λmax = 5.2541.We calculate the consistency index of the judgment matrix as follows:(13)CI=λmax−nn−1.Here, CI = 0.0635.The average random consistency index is shown in Table4.Table 4
Mean random consistency indicator.
Order,n123456789RI000.520.891.121.261.361.411.46We calculate the random consistency ratio as follows:(14)CR=CIRI.H CR = 0.0567 < 0.10.Therefore, it can be determined that WA = (0.1827, 0.0596, 0.2522, 0.0977, 0.4078) is the criterion layer weight that satisfies the consistency test conditions.


## 4.2.3. Calculation of Indicator Layer Weights

Using the same method as above, the standard layer judgment matrix weights are calculated as shown in Tables5–9, respectively.Table 5
The scoring results of the policy and legal risk indicator layer.
Policy and legal risk A1Industry policy risk a11Legal and regulatory risks a12Industry regulatory risk a13WiIndustry policy risk a1111/21/30.1717Legal and regulatory risks a12213/20.4414Industry regulatory risk a1332/310.3869Table 6
The scoring results of the industry competition risk index layer.
Industry competition risk A2Risk a21 of low-price competition among peersInfiltrator substitution risk a22Service homogenization risk a23WiRisk a21 of low-price competition among peers11/41/50.0994Infiltrator substitution risk a22412/30.3736Service homogenization risk a2353/210.5270Table 7
The scoring results of the information technology risk index layer.
Information technology risk A3Financial software technology risk a31Financial data access risk a32Internal information process risk a33WiFinancial software technology risk a311430.6300Financial data access risk a321/412/30.1515Internal information process risk a331/33/210.2185Table 8
The scoring results of the indicator layer for undertaking business risks.
Undertaking business risk A4Delegator moral hazard a41Risk a42 of loss of customer dataAccounting information distortion risk a43Service charge recovery risk a44WiDelegator moral hazard a41131/330.2664Risk a42 of loss of customer data1/311/51/20.0840Accounting information distortion risk a4335130.5083Service charge recovery risk a441/321/310.1413Table 9
Scoring results at the practitioner risk indicator layer.
Practitioner risk A5Professional skills risk a51Professional ethics hazard a52Employee training risk a53Liquidity risk a54WiProfessional skills risk a5113450.5325Professional ethics hazard a521/31330.2542Employee training risk a531/41/311/20.0911Liquidity risk a541/51/3210.1222λmax = 3.0735 and CR = 0.0707 < 0.10.Indicator layer weights for policy legal risks: WA1 = (0.1717, 0.4414, 0.3869).λmax = 3.0037 and CR = 0.0036 < 0.10.The indicator layer weight of industry competition risk: WA2 = (0.0994, 0.3736, 0.5270).λmax = 3.0015 and CR = 0.0014 < 0.10.Indicator layer weights for information technology risk: WA3 = (0.6300, 0.1515, 0.2185).λmax = 4.1315 and CR = 0.0493 < 0.10.Indicator layer weights for undertaking business risks: WA4 = (0.2664, 0.0840, 0.5083, 0.1413).λmax = 4.1471 and CR = 0.0551 < 0.10.The weight of the practitioner risk indicator layer: WA5 = (0.5325, 0.2542, 0.0911, 0.1222).


## 4.2.4. Calculation of Comprehensive Weight of Index Layer

According to the formula: the comprehensive weight of the indicator layer = the weight of the indicator layer × the weight of the criterion layer, the comprehensive weight of each indicator in the indicator layer of HIG can be obtained by calculation, as shown in Table10.Table 10
The comprehensive weight of the indicators of the HIG company’s indicator layer.
IndexPolicy and legal risk A1Industry competition risk A2Information technology risk A3Undertaking business risk A4Practitioner risk A5The comprehensive weight of the indicator layerRank the top three0.18270.05960.25220.09770.4078Industry policy risk a110.17170.0314Legal and regulatory risks a120.44140.0806Industry regulatory risk a130.38690.0707Risk a21 of low-price competition among peers0.09940.0059Infiltrator substitution risk a220.37360.0223Service homogenization risk a230.52700.0314Financial software technology risk a310.63000.15892Financial data access risk a320.15150.0382Internal information process risk a330.21850.0551Delegator moral hazard a410.26640.0260Risk a42 of loss of customer data0.08400.0082Accounting information distortion risk a430.50830.0497Service charge recovery risk a440.14130.0138Professional skills risk a510.53250.21711Professional ethics hazard a520.25420.10373Employee training risk a530.09110.0371Liquidity risk a540.12220.0498It can be found from Table10 that the top three comprehensive weights of the indicator layer are professional skills risk, financial software technology risk, and professional ethics risk.


## 4.3. Application of the Fuzzy Comprehensive Evaluation Method

### 4.3.1. Establishment of the Membership Matrix

Twenty experts selected Appendix B and obtained the evaluation frequency table after statistics, as shown in Table11.Table 11
Statistical table of frequency of satisfaction evaluation of five levels of risk factors.
Risk factorVery importantRelatively importantGenerally importantLess importantVery unimportantFrequencyFrequencyFrequencyFrequencyFrequencyPolicy and legal risk A146820Industry policy risk a1128820Legal and regulatory risks a1248620Industry regulatory risk a1326840Industry competition risk A226840Risk a21 of low-price competition among peers241022Infiltrator substitution risk a22061022Service homogenization risk a23221042Information technology risk A346820Financial software technology risk a3166422Financial data access risk a3228640Internal information process risk a3326840Undertaking business risk A444840Delegator moral hazard a4106842Risk a42 of loss of customer data26822Accounting information distortion risk a4328840Service charge recovery risk a4406842Practitioner risk A5261020Professional skills risk a5128820Professional ethics hazard a5226840Employee training risk a53061040Liquidity risk a54241022Taking the membership evaluation of a11 as an example, it is very important for 2 experts to choose a11; the choice of 8 experts is more important; the choice of 8 experts is generally important; the choice of 2 experts is not very important; and the choice of no experts is very unimportant. Then the membership degree of a11 is as follows: r11 = (0.1, 0.4, 0.4, 0.1, 0), and so on, the corresponding membership degree matrix can be obtained by obtaining the membership degree of each index.(15)R1=0.10.40.40.100.20.40.30.100.10.30.40.20,R2=0.10.20.50.10.100.30.50.10.10.10.10.50.20.1,R3=00.30.20.10.10.10.40.30.200.10.30.40.20,R4=00.30.40.20.10.10.30.40.10.10.10.40.40.2000.30.40.20.1,R5=0.10.40.40.100.10.30.40.2000.30.50.200.10.20.50.10.1,R=0.20.30.40.100.10.30.40.200.20.30.40.100.20.20.40.200.10.30.50.10.


### 4.3.2. Fuzzy Operations

Taking the criterion-level indicator of policy and legal risk as an example, according to formula (8), its membership algorithm is(16)B=W1·R1=0.1717,0.4414,0.3569·0.10.40.40.100.20.40.30.100.10.30.40.20.B1 = (0.1411, 0.3523, 0.3439, 0.1327, 0)The same can be obtained:B2 = (0.0626, 0.1847, 0.5, 0.1527, 0.1)B3 = (0.226, 0.3151, 0.2589, 0.137, 0.063)B4 = (0.0592, 0.3508, 0.4, 0.1916, 0.0492)B5 = (0.0909, 0.341, 0.4213, 0.1345, 0.0122)Normalized to get:B1 = (0.1455, 0.3632, 0.3545, 0.1368, 0)B2 = (0.0626, 0.1847, 0.5, 0.1527, 0.1)B3 = (0.226, 0.3151, 0.2589, 0.137, 0.063)B4 = (0.0563, 0.3338, 0.3807, 0.1823, 0.0468)B5 = (0.0909, 0.341, 0.4213, 0.1345, 0.0122)Target layer fuzzy evaluation results:B = W·R = (0.1533, 0.2902, 0.4408, 0.1157, 0)Using the corresponding scores of the previous evaluation set, the risk scores of each factor can be obtained by operation:B1 = 0.1455 × 20 + 0.3632 × 40 + 0.3545 × 60 + 0.1368 ×  80 = 49.65B2 = 0.0626 × 20 + 0.1847 × 40 + 0.5 × 60 + 0.1527 ×  80 + 0.1 × 100 = 60.86B3 = 0.226 × 20 + 0.3151 × 40 + 0.2589 × 60 + 0.137 ×  80 + 0.063 × 100 = 49.92B4 = 0.0563 × 20 + 0.3338 × 40 + 0.3807 × 60 +  0.1823 × 80 + 0.0468 × 100 = 56.58B5 = 0.0909 × 20 + 0.341 × 40 + 0.4213 × 60 + 0.1345 ×  80 + 0.0122 × 100 = 52.72B = 0.1533 × 20 + 0.2902 × 40 + 0.4408 × 60 + 0.1157 ×  80 = 50.38


## 4.3.1. Establishment of the Membership Matrix

Twenty experts selected Appendix B and obtained the evaluation frequency table after statistics, as shown in Table11.Table 11
Statistical table of frequency of satisfaction evaluation of five levels of risk factors.
Risk factorVery importantRelatively importantGenerally importantLess importantVery unimportantFrequencyFrequencyFrequencyFrequencyFrequencyPolicy and legal risk A146820Industry policy risk a1128820Legal and regulatory risks a1248620Industry regulatory risk a1326840Industry competition risk A226840Risk a21 of low-price competition among peers241022Infiltrator substitution risk a22061022Service homogenization risk a23221042Information technology risk A346820Financial software technology risk a3166422Financial data access risk a3228640Internal information process risk a3326840Undertaking business risk A444840Delegator moral hazard a4106842Risk a42 of loss of customer data26822Accounting information distortion risk a4328840Service charge recovery risk a4406842Practitioner risk A5261020Professional skills risk a5128820Professional ethics hazard a5226840Employee training risk a53061040Liquidity risk a54241022Taking the membership evaluation of a11 as an example, it is very important for 2 experts to choose a11; the choice of 8 experts is more important; the choice of 8 experts is generally important; the choice of 2 experts is not very important; and the choice of no experts is very unimportant. Then the membership degree of a11 is as follows: r11 = (0.1, 0.4, 0.4, 0.1, 0), and so on, the corresponding membership degree matrix can be obtained by obtaining the membership degree of each index.(15)R1=0.10.40.40.100.20.40.30.100.10.30.40.20,R2=0.10.20.50.10.100.30.50.10.10.10.10.50.20.1,R3=00.30.20.10.10.10.40.30.200.10.30.40.20,R4=00.30.40.20.10.10.30.40.10.10.10.40.40.2000.30.40.20.1,R5=0.10.40.40.100.10.30.40.2000.30.50.200.10.20.50.10.1,R=0.20.30.40.100.10.30.40.200.20.30.40.100.20.20.40.200.10.30.50.10.


## 4.3.2. Fuzzy Operations

Taking the criterion-level indicator of policy and legal risk as an example, according to formula (8), its membership algorithm is(16)B=W1·R1=0.1717,0.4414,0.3569·0.10.40.40.100.20.40.30.100.10.30.40.20.B1 = (0.1411, 0.3523, 0.3439, 0.1327, 0)The same can be obtained:B2 = (0.0626, 0.1847, 0.5, 0.1527, 0.1)B3 = (0.226, 0.3151, 0.2589, 0.137, 0.063)B4 = (0.0592, 0.3508, 0.4, 0.1916, 0.0492)B5 = (0.0909, 0.341, 0.4213, 0.1345, 0.0122)Normalized to get:B1 = (0.1455, 0.3632, 0.3545, 0.1368, 0)B2 = (0.0626, 0.1847, 0.5, 0.1527, 0.1)B3 = (0.226, 0.3151, 0.2589, 0.137, 0.063)B4 = (0.0563, 0.3338, 0.3807, 0.1823, 0.0468)B5 = (0.0909, 0.341, 0.4213, 0.1345, 0.0122)Target layer fuzzy evaluation results:B = W·R = (0.1533, 0.2902, 0.4408, 0.1157, 0)Using the corresponding scores of the previous evaluation set, the risk scores of each factor can be obtained by operation:B1 = 0.1455 × 20 + 0.3632 × 40 + 0.3545 × 60 + 0.1368 ×  80 = 49.65B2 = 0.0626 × 20 + 0.1847 × 40 + 0.5 × 60 + 0.1527 ×  80 + 0.1 × 100 = 60.86B3 = 0.226 × 20 + 0.3151 × 40 + 0.2589 × 60 + 0.137 ×  80 + 0.063 × 100 = 49.92B4 = 0.0563 × 20 + 0.3338 × 40 + 0.3807 × 60 +  0.1823 × 80 + 0.0468 × 100 = 56.58B5 = 0.0909 × 20 + 0.341 × 40 + 0.4213 × 60 + 0.1345 ×  80 + 0.0122 × 100 = 52.72B = 0.1533 × 20 + 0.2902 × 40 + 0.4408 × 60 + 0.1157 ×  80 = 50.38


## 4.4. Analysis of Risk Assessment Results

From the results of the fuzzy comprehensive evaluation, the influence of each risk factor in the criterion layer can be comprehensively analyzed; the degree of attention to the risk factors can be determined; and corresponding countermeasures can be formulated. Finally, analyze the main risk factors, focus on the top three risk factors ranked by the comprehensive weight of the indicator layer, and focus on the response.


## 5. Discussion

The main research methods of this study are the analytic hierarchy process and the fuzzy comprehensive evaluation method. Analytic hierarchy process is a decision analysis method that combines qualitative and quantitative analysis to solve complex multiobjective problems; the relative importance of each decision-making scheme is given; the weight of each standard of each decision-making scheme is reasonably given; and the weights are used to obtain the superior and inferior order of each scheme, which can be effectively applied to those problems that are difficult to solve by quantitative methods. The fuzzy comprehensive evaluation method is a comprehensive evaluation method that transforms qualitative evaluation into quantitative evaluation through the membership degree theory of fuzzy mathematics. The above two methods are greatly influenced by personal subjectivity, have certain limitations, and need to be improved.


## 6. Conclusions

There are now few small- and medium-sized bookkeeping firms, and the industry’s future prospects are unclear. Future social and economic development are inextricably linked to long-term sustainable development. As a result, there are fewer studies on these organisations that are relevant, and risk management studies are more beneficial. This study uses an analytic hierarchy process and a fuzzy comprehensive assessment approach to successfully combine quantitative and qualitative analysis and create a multilevel analysis structure model of the risk management evaluation index system of small- and medium-sized agency accounting firms. The specific risk score of each factor is calculated through the scores of 20 experts, and the importance of risk is judged according to the size of the score, which helps the company formulate corresponding risk measures. This research provides a reference for the risk management of enterprises in this industry and has certain research value.



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*Source: 8701591-2022-08-13.xml*