## Materials and Methods  
### Capability Gap Based Value Decision  
#### 2.1.1 Weight Decision Based on Correlation Analysis  
Weight information determines the criteria importance, and thus influences the final evaluation results of systems portfolios. Typically, criteria weights tend to be determined according to expert experience, which is criticized for its subjectivity and infeasibility. Correlation analysis is a quantitative method to measure the correlations between independent and dependent variables, and therefore can be used to indicate the weights of independent variables. The maximal information coefficient (MIC) is used to measure correlations among all kinds of data. Compared to other measurements, it is acknowledged that the MIC is more sensible to identify correlations among variables, whatever for linear relations or non-linear relations (cubic, exponential, sinusoidal, parabolic, etc.) The correlation of variable \(X\) and \(Y\) can be indicated by the mutual information, as Equation (1) shows. \[I(X,Y)=\sum_{x,y}p(x,y)\log\frac{p(x,y)}{p(x)p(y)}, \tag{1}\]  
Because the information entropy of discrete random variables is denoted as \(H(p)=-\sum_{i=1}^{n}p_{i}\log p_{i}\), where \(\sum_{i=1}^{n}p_{i}=1\). Therefore, the \(I(X,Y)\) can be proved to be equivalent to Equation (2). \[ \begin{array}{ll}I(X,Y)&=H(X)+H(Y)-H(X,Y)\\ &=H(X)-H(X|Y)\\ &=H(Y)-H(Y|X)\end{array} , \tag{2}\]  
With respect to MIC, it is assumed that the \(D=X\times Y\subset\mathbb{R}^{2}\) is the variable space. Dividing the \(D\) into a grid \(G\) of \(x\times y\). The distribution of data \(D\) in grid \(G\) is represented by \(D|_{G}\). Executing multiple divisions on \(D\) and calculating the \(I(D|_{G})\) under different divisions. Then, the MIC can be obtained by calculating the \(\max\,I(D|_{G})\) value from all possible division schemes. Here, a grid of one row and one column is taken for example as Figure 1 shows. All data points are divided into four areas: top left, top right, bottom left, and bottom right. The numbers of data points belonging to each area are 1, 4, 4, and 1. Then, the normalized numbers of data point frequencies in the four regions are 0.1, 0.4, 0.4, and 0.1. Herein, \(X\) has two values: left and right, and \(Y\) has two values: upper and lower. The joint probabilities of the data in four regions can be calculated as \(p(X=left,Y=up)=0.1\), \(P(X=right,Y=up)=0.4\), \(P(X=left,Y=down)=0.4\), \(P(X=right,Y=down)=0.1\). Therefore, the point frequencies in X, Y are \(P(X=left)=0.5\), \(P(X=right)=0.5\), \(P(Y=upper)=0.5\) and \(P(Y=lower)=0.5\). According to the mutual information calculation formula introduced above, the mutual information of \(X\) and \(Y\) is obtained as Equation (3). \[ \begin{array}{c}p(X=left,Y=up)\log\left(\frac{p(X=left,Y=up)}{p(X=left,Y= up)}\right)\right.\\ \left.+p(X=left,Y=up)\log\left(\frac{p(X=left,Y=up)}{p(X=left,Y=up)}\right) \right.\\ I(X,Y)=+p(X=left,Y=up)\log\left(\frac{p(X=left,Y=up)}{p(X=left,Y=up)}\right) \right.\\ \left.+p(X=left,Y=up)\log\left(\frac{p(X=left,Y=up)}{p(X=left,Y=up)}\right) \right.\\ \left.+p(X=left,Y=up)\log\left(\frac{p(X=left,Y=up)}{p(X=left,Y=up)}\right) \right.\\ \left.=0.1\times\log\left(\frac{0.1}{0.5\times 0.5}\right)+0.4\times\log\left( \frac{0.4}{0.5\times 0.5}\right)+0.4\times\log\left(\frac{0.4}{0.5\times 0.5} \right)+0.1\times\log\left(\frac{0.1}{0.5\times 0.5}\right)\right.\end{array} , \tag{3}\]  
By using the traversal algorithm, we can find the maximal value from all possible division schemes as \(\Gamma(D,\,x,\,y)=\max\left(D\right|_{G}\right).\) Then, the characteristic matrix \(M(D)_{x,y}\) is constructed through normalization operation on \(\Gamma(D,\,x,\,y)\) as \(M(D)_{x,y}=\Gamma(D,\,x,\,y)/\log\min\left[x,\,y\right]\). Whereupon the MIC can be obtained according to \(MIC(D)=\max\limits_{x,y\in E(n)}\left[M(D)_{x,y}\right]\).