## 4 Evaluation Technique of Database Security
Each of these functions can be represented as follows:  
* Linear Z-shaped membership function of a fuzzy set \(A_{\text{L}}=\{\mu_{\text{L}}(x)/x\}\), corresponding to a fuzzy variable \"L\" for a linguistic variable \(P_{t}\): \[\mu_{\text{L}}(x;a,b)=\left\{ \begin{array}{ll}1,&x\leq a,\\ \frac{b-x}{b-a},&a<x<b,\\ 0,&b\leq x,\end{array} \right.\] (6) where \(a,b\) are numeric parameters (\(a\leq b\));
* Trapezoidal membership function of a fuzzy set \(A_{\text{M}}=\{\mu_{\text{M}}(x)/x\}\) corresponding to a fuzzy variable \"M\" for a linguistic variable \(P_{t}\): \[\mu_{\text{M}}(x;a,b,c,d)=\left\{ \begin{array}{ll}0,&x\leq a,\\ \frac{x-d}{b-a},&a\leq x\leq b,\\ 1,&b\leq x\leq c,\\ \frac{d-x}{d-c},&c\leq x\leq d,\\ 0,&d\leq x,\end{array} \right.\] (7) where \(a,b,c,d\) are numeric parameters (\(a\leq b\leq c\leq d\));
* Linear S-shaped membership function of a fuzzy set \(A_{\text{H}}=\{\mu_{\text{H}}(x)/x\}\) corresponding to a fuzzy variable \"H\" for a linguistic variable \(P_{t}\): \[\mu_{\text{H}}(x;c,d)=\left\{ \begin{array}{ll}0,&x\leq c,\\ \frac{x-c}{d-c},&c<x<d,\\ 1,&d\leq x,\end{array} \right.\] (8) where \(c,d\) are numeric parameters (\(c\leq d\)). Figure 2 shows all three graphs of the membership functions of fuzzy variables used to determine the linguistic variable--the likelihood of a threat occurrence \(P_{t}\). The expert based on a priori knowledge assigns linguistic values, which are the names of fuzzy variables, for each the likelihood of a threat occurrence \(P_{t_{i}}\), as a component of the corresponding specific barrier \(b_{I}\). In this case, these values can be represented verbally as \"low likelihood\", \"moderate likelihood\", \"high likelihood\" (or \"L\", \"M\", \"H\"). At that, since each such value is associated with the corresponding membership function with the corresponding approximate quantitative estimates, then, in principle, for each threat \(t_{i}\in T\), it is possible to determine with a limited degree of accuracy the numerical value of this likelihood \(P_{t_{i}}\), for example, as the _modal value_ of a fuzzy set. If the core of a fuzzy set \(A\) (is the crisp subset of the domain \(X\) consisting of all elements of \(A\) with a membership grade equal to one [72]: \(C(A)=core(A)=\{x:\mu_{A}(x)=1,x\in X\}\)) contains more than one element, then for such a set the modal value is calculated as the mean value of the core. Further, using the above approach, we represent in the form of the corresponding linguistic variable--the likelihood of exploiting the vulnerability--\(P_{Y}\) (the likelihood that in the event of implementing threat in relation to an asset, this threat will be successfully implemented using this vulnerability). To estimate \(P_{Y}\), we introduce three verbal gradations with the corresponding approximate quantitative estimates:  
* High (H). The vulnerability is easy to exploit and there is weak protection or no protection at all. The likelihood of exploiting a vulnerability (the likelihood of successful implementation of a threat due to a given vulnerability) is in the range [0.7, 1];
* Moderate (M). The vulnerability can be exploited, but there is some protection. The likelihood of exploiting a vulnerability is in the range [0.3, 0.7];
* Low (L). The vulnerability is difficult to exploit and there is good protection. The likelihood of exploiting a vulnerability is in the range [0, 0.3]. As with threats, this three-tier scale may be sufficient for an initial high-level evaluation of the vulnerability. In the future, for a more detailed evaluation, the authors also plan to expand it. Then, using the introduced designations, we define the names of fuzzy variables (\(\beta_{\varepsilon}\), where \(\varepsilon\in\mathbb{N}^{*}_{<n}\)) is the set of values of the term-set \(T_{\gamma}\) for the linguistic variable \(P_{\gamma}\): \(T_{\gamma}\) = (\"high vulnerability\", \"moderate vulnerability\", \"low vulnerability\") = (\"H\", \"M\", \"L\"), that is, \(\beta_{1}\) = \"H\", \(\beta_{2}\) = \"M\", \(\beta_{3}\) = \"L\".