# Towards Design and Development of Security Assessment Framework for Internet of Medical Things
## 3 Security Assessment of IoMT
### Integrated Fuzzy AHP-TOPSIS Method
\[r_{i}=\left(\text{a}_{ij}^{1}\times\text{a}_{ij}^{2}\ldots\text{a}_{ij}^{10} \right)^{\frac{1}{10}} \tag{2}\]  
Step 4: Every criterion's weight is assigned. This is accomplished by normalizing the matrix. \[w_{i}=r_{i}\times(r_{1}+r_{2}+r_{3}+\ldots+r_{n})^{1} \tag{3}\]  
Step 5: For every weight, the Best Non-Fuzzy Performance (BNPP) significance is decided. A weight's BNP value (\(l\), \(m\), \(u\)) is provided by the following equation. \[\text{BNP value }=\frac{[(u-l)+(m-l)]}{3+l} \tag{4}\]  
Step 6: Standards are consistently rated according to their BNP values. When comparing criteria, the standard with the higher BNP value is thought to have a bigger influence. Fuzzy TOPSIS: The main idea behind the TOPSIS strategy is that the best suggested choice must not only be the closest to the positive ideal solution (PIS) but also be the furthest away from the negative ideal solution (NIS) [40; 41; 42; 43; 44; 45; 46]. TOPSIS has the benefit of requiring only restricted subjective input from decision makers as well as the strategy's ability to speedily determine the best alternate solution. The following are the stages involved in the fuzzy TOPSIS method. Step 1: Standard weights are acquired from fuzzy AHP. The weight values of every characteristic under evaluation are included in the fuzzy AHP outcome. Step 2: A fuzzy assessment matrix is produced. TFNs are used as transactions to summarize decision makers' judgments of attributes for every decision alternative that corresponds to each set of criteria. Step 3: The fuzzy judgment matrix is standardized. The term R represents the normalized fuzzy decision matrix, and its elements are \(\left[r_{i}\right]_{m\times n}\); \(i=1,2,3,\ldots,m\), where \(m\) is the complete number of criteria. \[\widetilde{r}_{ij}=\left(\frac{l_{ij}}{u_{j}^{+}},\frac{m_{ij}}{u_{j}^{+}}, \frac{u_{ij}}{u_{j}^{+}}\right) \tag{5}\]  
where \(u_{j}^{+}\) is the highest value in the whole fuzzy decision matrix. Step 4: The points of reference for the fuzzy positive ideal as well as the fuzzy negative ideal are ascertained. The area compensation tactic defines fuzzy positive ideal solutions (FPIS) as well as fuzzy negative ideal solutions (FNIS). \[\text{FPIS }A^{+}=\left(v_{i}^{+}\ldots v_{j}^{+}\ldots v_{n}^{+}\right) \tag{6}\]  
\[\text{FNIS }A^{-}=\left(v_{i}^{-}\ldots v_{j}^{-}\ldots v_{n}^{-}\right) \tag{7}\]  
where \(v_{i}=(1,1,1)\times\left(w_{j}\right)\). Step 5: The distance from FPIS (d\({}^{+}\)) and the distance from FNIS (d\({}^{-}\)) are recognized with the help of the following equations. \[\text{D}_{j}^{+}=\sum_{j=1}^{n}\text{d}(\widetilde{v}_{ij},\widetilde{v}_{j}^ {*})\ i=1,2,\ldots,\text{m} \tag{8}\]  
\[\text{D}_{j}^{-}=\sum_{j=1}^{n}\text{d}(\widetilde{v}_{ij},\widetilde{v}_{j}^ {-})\ i=1,2,\ldots,\text{m} \tag{9}\]  
where d(a, b) is the range between two fuzzy figures, a and b. It is demarcated as  
\[\text{d}\left(\widetilde{a},\widetilde{b},\right)=\sqrt{\frac{1}{3}\Big{[} \left(\text{a}_{1}-\text{b}_{1}\right)^{2}+\left(\text{a}_{2}-\text{b}_{2} \right)^{2}+\left(\text{a}_{3}-\text{b}_{3}\right)^{2}\Big{]}} \tag{10}\]  
Step 6: The relative proximity to the ideal value is calculated, and the alternative solutions are ranked correspondingly. The relative proximity is provided through the following equation. \[\widetilde{CC}_{i}=\frac{\text{d}_{i}^{-}}{\text{d}_{i}^{+}+\text{d}_{i}^{-}} \tag{11}\]