# Roadmap Modeling and Assessment Approach for Defense Technology System of Systems
## 3 Roadmap Modeling and Assessment Approaches
### Assessment Approaches  
Based on the foregoing models, two assessment approaches, focusing on the contribution rate to satisfy the requirements and the importance of knowledge diffusion, are proposed. First, the analytic hierarchy processes (AHP) method was introduced to evaluate the contribution rate of technology alternatives using the requirement decomposed structure mentioned above [29]. The detail process is displayed as follows. 1. Investigate the judgement matrix \(A_{n\times n}^{ij}\) involving \(n\) elements which stay in the \(i\)th layer and belong to the \(j\)th father node. By comparing the element pairs with related support intelligence and calibrated expertise, one can measure the relative importance using the 1-9 score rank. 2. Compute the maximum eigenvalue and its corresponding eigenvector \(e^{ij}\) of the judgement matrix \(A_{n\times n}^{ij}\). 3. Calculate the assessment result of the contribute rates. The contribute rate of the \(l\)th element is defined as \(C_{l}^{i}=C_{l}^{i}+e_{l}^{ij}\times C_{j}^{i-1}\) when the value of its father node is \(C_{j}^{i-1}\). \begin{table}
\begin{tabular}{c c c c} \hline
**Stakeholders** & **Related Elements** & **Requirement Models** & **Outline** \\ \hline Strategic decider & Security strategy & Strategic game models & This model focuses on hotspot security issues, including strategic objectives, tactics, and capabilities \\ Military officer & Military capability & & \\ Military officer & Military capability & & \\ Weapons engineer & Weapons & Combat network models & This model consists of different types of nodes representing weapons function and edges referring to their interrelations \\ Weapons engineer & Weapons & & \\ Technology researcher & Technology & Technology impact matrices & This model collects the core functional indices of weapons, and measures the impacts of technology on those selected indices \\ \hline \end{tabular}
\end{table} 
Table 1: Requirement analysis models for defense technologies. In the algorithm above, the assessment of root node \(C^{0}\) is initialized as 1 and others are set as 0. Additionally, one should not update the values of the elements in the \(i\)th layer until the assessment of their father nodes has been completed. Second, the authors investigated the knowledge diffusion among the dual-layer citation network. Based on the network topological structure, an approach to assess the node importance of spreading property combining the eigenvector centrality [30] and PageRank value [31] is put forth. The detail process is displayed as follows. * Compute the eigenvector centrality vector \(x\): \(x=\lambda^{-1}A^{a}x\) of the sub-network in the article layer. The \(A^{a}\) refers to the adjacency matrix of the mentioned network and the \(\lambda\) is its maximum eigenvalue. * Assign the values of two parameters, namely the inter-layer and intra-layer diffusion strength factors \(\alpha\) and \(\beta\). Then, one can construct the universal citation network \(A^{u}\), where \(A^{u}_{ij}=\alpha(A^{a}_{ij}+A^{p}_{ij})+\beta A^{a-p}_{ij}\), by extending and integrating the article-layer sub-network \(A^{a}\), article-patent inter-layer sub-network \(A^{a-p}\), and patent-layer sub-network \(A^{p}\). * Initialize the node importance values. The initial value of the \(i\)th article node is set as \(PR_{i}(0)=x_{i}/\sum\limits_{j=1}^{n}x_{j}\) and the patent nodes' values are assigned as 0. * Calculate the elements of the revised row stochastic matrix \(R^{u}_{ij}\) using the algorithm below. \[R^{u}_{ij}=\left\{ \begin{array}{l}1/k^{out}_{i},\;if\;k^{out}_{i}>0\wedge A ^{u}_{ij}>0\\ 0,\;if\;k^{out}_{i}>0\wedge A^{u}_{ij}=0\\ 1/n,\;if\;k^{out}_{i}=0\end{array} \right..\] (1) where the \(k^{out}_{i}\) represents the out-degree of the \(i\)th node in \(A^{u}\) while \(n\) refers to its node count. * Select a parameter \(s\) to measure the randomness in knowledge diffusion. Then, compute the assessment values of node importance using the following iterative algorithm, where \(k\) is the given iteration number.