# Smart City Actions Integrated into Urban Planning:
## 3 Materials and Methods
DEMATEL evaluates a hierarchical structure based on expert opinion to determine the influence levels between thematic areas  
Figure 2: Database review protocol. with a relation matrix and vector calculation [32]. The hierarchy influence degree, along with the direction and intensity of the relations, is structured using a cause-and-effect relationship diagram [33]. DEMATEL is composed of five phases: In phase 1, the direct influence matrix was developed with the experts' responses on the relationships between the 11 thematic areas. An initial average matrix \(A\) was generated, where each element (_aij_) indicates the average degree of influence that a thematic area \(i\) exerts on a thematic area \(j\) from all \(n\) thematic areas. Phase 2 involved calculating the normalized influence matrix \(X\), by normalizing the initial average matrix \(A\) by the normalization factor \(k\) (Equations (1) and (2)), where \(k\) is the normalization factor. \[X=k.A \tag{1}\]  
\[k=\frac{1}{max_{1\leq i\leq n}\sum_{j=1}^{n}{\it aij}}\,\ i,\ j=1,2,\ldots,n \tag{2}\]  
In phase 3, to construct the total relationship matrix \(T\), the identity matrix \(I\) was initially constructed to mirror the elements of the normalized matrix, from which the total relationship matrix \(T\) was structured (Equation (3)), where \(T\) is the total matrix and \(I\) is the identity matrix. \[T=X(I-X)^{-1} \tag{3}\]  
When executing phase 4, rows and columns were added to the total matrix \(T\) to perform the calculation of vectors \(D\), which included the sum per row and the vector \(R\), totaling the sum per column, where \(t\) corresponds to element \(t\) of row \(i\) and column \(j\) (Equations (4)-(6)). \[T=\left[\ {\it ij}\right]_{nxn},i,j=1,\ 2,\ldots,n \tag{4}\]  
\[D=\left[\ {\sum_{j=1}^{n}{\it tij}}\ \right]_{nx}=\left[\ t_{i}\ \right]_{nx1} \tag{5}\]  
\[R=\left[\ {\sum_{j=1}^{n}{\it tij}}\ \right]_{1x}=\left[\ t_{i}\ \right]_{1 xn} \tag{6}\]  
In phase 5, based on \(D\) and \(R\), vectors were calculated by axes, with the horizontal axis being vector (\(D+R\)) and the vertical axis being vector (\(D-R\)). The \(D+R\) value coordinates, identified on the abscissa axis, classify the thematic areas by importance level, while the \(D-R\) value coordinates, on the ordinate axis, classify the thematic areas by their level of influence on urban spaces. After calculating the vectors, the points found were identified in the cause-and-effect diagram (\(D+R\), \(D-R\)), by quadrant, as described in [33], and then classified into central, determining, independent, and impact factors for decision-making (Figure 3). Figure 3: Cause-and-effect diagram structure. Source: adapted from [33]. The data were systematized and organized for analysis and interpretation, using a matrix structure and the threshold values' quantification, while considering the cause-and-effect diagram's graphical coordinates. Also, the points found were divided into four quadrants, with the \(D+R\) values dividing the diagram vertically, in order of importance, and the \(D-R\) values enabling the classification of points by influence level, on the horizontal axis. For the seventh stage of the design science research, the construct was structured, including a proposal for ranking thematic areas for smart cities' performance, where the scores of the \(11\) thematic areas were normalized, serving as support for guiding smart cities' action planning.