**5. Weighting the risks of authorized certification bodies by fuzzy DEMATEL method**

Within the scope of the study, the main risks that may be encountered in certification bodies authorized by VQA and sub-risks related to these risks were determined, and these risks were confirmed by the lead auditors in the audit of certification bodies. The weights of the risks were calculated using the "Fuzzy DEMATEL Method" introduced in the previous section.

Step 1: Demonstrating the relationship between risks

The network structure of the model is presented in the Figure below (**Figure 1**). The relations between the main criteria and the sub-criteria are shown in the network structure of the model. As a result of the evaluation made with the expert group, it was evaluated that all the criteria were in interaction with each other.

Step 2: Designing the questionnaire

A questionnaire consisting of two parts was designed for the application of the fuzzy DEMATEL method. In the first part of the questionnaire, in order to determine the relations between the main criteria, and in the second part, in order to determine the relations between the sub-criteria under each main criterion group, matrices were designed to allow pairwise comparison. Questionnaires were asked to make pairwise comparisons using these matrices and to determine whether the risks affect each other. The questionnaire was administered to a group of experts consisting of 12 people. The expert group was selected from people who are in charge as lead auditors in VQA audits and had sufficient knowledge and experience in assessment and certification and audit activities.

Step 3: Calculating the inconsistency rate of the questionnaire results

The inconsistency rate of the obtained data was determined in accordance with the formula for the calculation of the inconsistency rate presented within the scope of a study conducted by Wang and Tzeng in 2012 [35]. The formula is presented below;

$$\text{Inconsistency rate} = \frac{1}{n(n-1)} \sum\_{i=1}^{n} \sum\_{j=1}^{n} \frac{\left| a\_{ij}^p - a\_{ij}^{p-1} \right|}{a\_{ij}^p} \times 100\text{\%} \tag{14}$$

**Figure 1.** *Relations between main and sub-risk criteria.*

*Development of a Risk Management Model by the Fuzzy DEMATEL Method in the Evaluation… DOI: http://dx.doi.org/10.5772/intechopen.110018*

n = Number of criteria

p = Number of experts

a p ij ¼ average of data from p experts for each pairwise comparison

a p�1 ij ¼ average of data from p � 1 experts for each pairwise comparison

If the inconsistency rate is <5%, the obtained data is determined to be consistent.

In line with the formula presented above, it has been determined that the data obtained as a result of the calculations made for the main criteria and the sub-criteria defined under the main criteria are consistent. Consistency rates are presented in **Table 3**. Since the consistency ratios of all criteria are less than 0.05, it is seen that the data are consistent.

Step 4: Conversion of survey data to fuzzy numbers

The data obtained as a result of pairwise comparisons made by each member of the expert group for the main criteria and sub-criteria were converted into fuzzy numbers. The triangular fuzzy values in **Table 1** were used to transform the data into fuzzy numbers.

Step 5: Utilizing CFCS (Converting Fuzzy Data into Crisp Scores) defuzzification method to defuzzifying fuzzy numbers and creating the initial matrix.

The normalization process was carried out by using the CFCS method steps presented in Eqs. (1)–(10). As a result of the calculations, xls and xrs matrices were obtained for both the main risk criteria group and the sub-risk criteria groups under


**Table 3.**

*Consistency rate of the data obtained from the expert group for the main criteria and sub-criteria.*


**Table 4.**

*Initial direct-relation matrix for main risk criteria (A).*

the main risk criteria group. By using these matrices, the total normalized value and the crisp value were calculated.

After obtaining the crisp values, the initial direct-relation matrices were calculated using Eq. (10). The initial direct-relation matrix obtained for the main risk criteria is presented in **Table 4** for illustrative purposes. The same calculations were made for the sub-risk criteria groups.

Step 6: Obtaining the normalized direct-relation matrix

Normalized direct-relation matrices were obtained by using Eq. (11). The normalized matrix obtained for the main risk criteria is presented in **Table 5** for illustrative purposes. The same calculations were made for the sub-risk criteria groups.

Step 7: Obtaining the total-relation matrices

Using Eq. (12), the total-relation matrices were calculated. The total relation matrix obtained for the main risk criteria is presented in **Table 6**. Total relation matrices were also obtained for the sub-risk criteria groups.

Step 8: Identifying cause and effect groups

The sum of the rows in the T matrix is shown with ri and the sum of the columns with cj, and the cause and effect groups are determined by calculating the values of "ri – cj" and "ri + cj". The cause and effect groups calculated for the main risk criteria are presented in **Table 7**. Similarly, cause and effect groups were calculated for the subrisk criteria groups.

A threshold value has been determined in order to avoid the complexity of the criteria with a small effect level. The threshold value was calculated by averaging the values in the total relationship matrix and 0.07 was obtained for the main risk criterion total relationship matrix.


**Table 5.**

*Normalized direct-relation matrix for main risk criteria (D).*


#### **Table 6.**

*Total relation matrix for main risk criteria (T).*

*Development of a Risk Management Model by the Fuzzy DEMATEL Method in the Evaluation… DOI: http://dx.doi.org/10.5772/intechopen.110018*


#### **Table 7.**

*Cause and effect groups for main risk criteria.*

Criteria below the threshold value were determined as affected (effect) criteria, and criteria above the threshold value were determined as affecting (cause) criteria [33].

Values below the threshold value of 0.07 for the main risk criterion total relationship matrix are shown with "-" and presented in **Table 8**. Similarly, threshold values were calculated for the sub-risk criteria groups.

According to the values in **Table 8**, a cause and effect diagram was produced for the main risk criterion matrix, which is shown in **Figure 2**. Similarly, cause and effect diagrams were produced for the sub-risk criteria groups.


#### **Table 8.**

*Illustration of values above and below the threshold value.*

**Figure 2.** *Cause and effect diagram for the main risk criterion matrix.*

Step 9: Calculation of criterion weights

Main risk criteria weights and sub-risk criteria weights were calculated using Eq. (13) and the results are presented in **Table 9**. The final weights were obtained by multiplying the weights of the main criteria and the weights of the sub-criteria. The final weights are shown in **Table 9**.

Step 10: Classification of criteria

Based on the criteria weights, the criteria were classified as high-, moderate-, and low-risk groups together with the expert group. While making this classification, risks with a value between 0 and 0.035 were included in the low-risk group, risks with a value between 0.035 and 0.045 were included in the moderate-risk group, and finally risks with a value above 0.045 were included in the high-risk group. The risk groups according to the weights of the criteria are shown in **Table 10**.


#### **Table 9.**

*Table showing main criterion weights, sub-criteria weights, and final weights.*

**No Sub criteria Definition of risk criteria Final weight Risk group** 1 A3 Assessors and internal verifiers do not have sufficient knowledge and experience. 0,054 High 2 F4 Failure to take adequate precautions for reliable assessment 0,053 High 3 A2 Failure of the assessor and internal verifiers to meet the assessor criteria 0,050 High 4 A4 Lack of awareness of the assessor and internal verifiers about the system 0,048 High 5 B4 Failure to perform assessment activities accurately, consistently, and reliably 0,046 High 6 B3 Assessor's failure to conduct exams in accordance with scenarios, checklists, and national qualifications 0,045 High 7 B1 The method used in theoretical and performance-based exams is not compatible with the qualifications. 0,044 Moderate 8 B5 Failure to make correct, consistent, fair, and reliable certification decisions 0,044 Moderate 9 F1 Lack of awareness of assessor and internal verifiers for consistent and fair assessment. 0,043 Moderate 10 F2 Possible conflicts of interest between assessors and candidates 0,042 Moderate 11 F3 The internal verifier has a conflict of interest with the candidate or assessor 0,042 Moderate 12 B2 Failure to conduct theoretical and performance-based exams in accordance with the guidelines 0,041 Moderate 13 D1 Not creating enough questions to meet the knowledge statements in the annex of the qualification units 0,039 Moderate 14 D2 The question booklets do not contain sufficient numbers and quality of questions to meet the knowledge statements. 0,039 Moderate 15 D3 Scenarios and checklists do not meet the skills and competencies in the annex of the qualification units 0,039 Moderate 16 D4 Failure to verify the suitability of materials used in assessment processes 0,039 Moderate 17 C2 Failure to perform internal verification activities in accordance with national qualifications 0,039 Moderate 18 C1 Failure to operate internal verification activity for each national qualification, qualification unit, and assessor 0,038 Moderate 19 C3 Failure of internal verifiers to make accurate, consistent, and fair assessments 0,037 Moderate 20 C4 Inadequate creation of the sampling plan in internal verification activities 0,035 Moderate 21 E4 Failure to take adequate measures to ensure the reliability of equipment 0,029 Low 22 C5 Failure to take corrective actions for detected nonconformities within the scope of internal verification 0,029 Low 23 E1 Inadequate physical environments to measure skills and competencies 0,027 Low

*Development of a Risk Management Model by the Fuzzy DEMATEL Method in the Evaluation… DOI: http://dx.doi.org/10.5772/intechopen.110018*


**Table 10.**

*Risk groups to which the criteria belong.*
