## 3 Risk Assessment-Based Dynamic Access Model
### Request a Risk Assessment
#### 3.1.3 Indicator Weight Calculation  
The accuracy of the evaluation results depends on the scientificity and rationality of the index weights. The traditional method for establishing indicator weights is to assign initial values based on experience and then continuously revise them according to the actual situation. However, due to the variability and uncertainty of the actual situation, this method is not only time-consuming but also the results obtained are not necessarily accurate. For this reason, this paper adopts the analytic hierarchy process in the multi-attribute decision-making related theory to assign the weights of the indicators. In the scenario of this paper, due to the correlation between the various attribute evidence in the risk analysis, this paper introduces the Fuzzy Analytic Hierarchy Process (FAHP) [30] to quantify the risk of the access request so as to construct an integrated multivariate access request security risk assessment model. This method not only reduces the subjective impact of its process but also takes into account the correlation of risk factors, making the assessment more objective and credible. FAHP is an improvement to the Analytic Hierarchy Process (AHP) [31], which solves the problem of repeatedly adjusting and testing the judgment matrix in the consistency test of the traditional AHP. This method first divides the target into \(n\) attributes. Then, these attributes are divided into several detailed pieces of evidence, which are the direct reflection of the attributes, thereby simplifying the dynamics and uncertainty of cloud computing user behavior. Corresponding to this paper, the risk objectives are divided into main attributes, resource attributes, and environmental attributes. Each attribute is further divided into several pieces of evidence that can be obtained by the system. The related FAHP concepts are briefly explained in the following. **Definition 1**. : _The fuzzy matrix \(A\) is defined as \(A=(a_{ij})_{n\times n},\Omega=\{1,2,...,n\}\), if there is \(0\leq a_{ij}\leq 1(i,j\in\Omega)\)._  
**Definition 2**. : _The fuzzy complementary matrix is defined as \(A=(a_{ij})_{n\times n},\Omega=\{1,2,...,n\}\), if there is \(a_{ij}+a_{ji}=1;\forall i,j\in\Omega\)._  
**Definition 3**. : _The fuzzy consistency matrix is defined as \(A=(a_{ij})_{n\times n},\Omega=\{1,2,...,n\}\), if there is \(a_{ij}=a_{ik}-a_{jk}+0.5;\forall i,j\in\Omega\)._  
**Theorem 1**. : _The matrix \(R=(r_{ij})_{n\times n}\) obtained by converting the fuzzy complementary matrix \(A\) according to Equations (3) and (4) must also be fuzzy._  
\[r_{i}=\sum_{k=1}^{n}a_{ik},i=\{1,2,...,n\} \tag{3}\]  
\[r_{ij}=\frac{r_{i}-r_{j}}{2(n-1)}+0.5 \tag{4}\]  
Assuming that in the risk assessment index, the attribute layer element groups are \(\{B_{1},B_{2},...,B_{n}\}\), and there are evidence layer elements \(\{B_{i1},B_{2},...,B_{in}\}\) in the attribute \(B_{i}\), and \(n\) is the number of evidence layer elements in the attribute \(B_{i}\), taking the risk \(T\) as the target, compare the influence degree of the attribute layer and evidence layer elements on the target. Based on the influence degree of each attribute on risk, this paper uses the \"1\(\sim\)9 value\" method of [PERSON] [30] to determine the importance ratio of two elements. [PERSON] the rationality of the \"1\(\sim\)9\" scale with a large number of experiments, and the \"1\(\sim\)9\" method has been recognized and widely used. The scale meanings are shown in Table 2.  
(1) Evidence Layer--Attribute Layer:  
According to Table 2, construct the initial judgment matrix \(EQ\) of the evidence layer:  
\[EQ=\left\{ \begin{matrix}a_{11}&a_{12}&\dots&a_{1n}\\ a_{21}&a_{22}&\dots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{n1}&a_{n2}&\dots&a_{nm}\end{matrix} \right\}\]  
Then the initial judgment matrix \(EQ\) is transformed into the fuzzy consistency matrix \(Q\) according to Equations (3) and (4):  
\[Q=\left\{