## 2 Model Formulation
### Rough Set and Improved TOPSIS Construction Sequence Sub-Model  
The problem of deciding the construction sequence of URT lines can be described in mathematical terms as follows: there are \(m\) lines in a URT network, and there are \(n\) attributes affecting the sequence of line construction; by comprehensively considering all \(n\) attributes, the construction sequence of all \(m\) lines is determined. Thus, the problem of deciding the construction sequence of URT lines belongs to ranking alternatives of MCDM (Multiple Criteria Decision Making) problems. At present, there are many methods available for solving the problems of this type, for example TOPSIS (The Technique for Order Preference by Similarity to an Ideal Solution), AHP (Analytic Hierarchy Process), SAW (Simple Additive Weighting), COPRAS (Complex Proportional Assessment), ELECTRE (ELimination Et Choix Traduisant la REalite), and so on [24]. TOPSIS offers several advantages over other approaches, such as strong adaptability and easy implementation and decision making [25]. It has been demonstrated to be one of the best methods for solving ranking issues and is used in many research fields [26; 27; 28; 29; 30]. Recently, TOPSIS has also begun to be applied in the field of transportation planning, in areas such as transportation system evaluation [31; 32], the ranking of urban traffic system performance [33], and ranking of the importance of URT network nodes [34]. However, the TOPSIS method has some limitations, for example, qualitative decision making attribute weight problems, and it sometimes fails to rank alternatives. The following improvements have been made in this study. 1. The weightings used in the TOPSIS method are determined using qualitative methods, such as expert scoring (ES), and weighted arithmetic average (WAA). This will affect the accuracy of the ranking results. Since Rough Set theory was first proposed by [PERSON] in 1982 [35; 36], it has been used to improve the weight problem in many studies [37; 38; 39]. In this study, the Rough Set classification mechanism was used to intelligently calculate the attribute weight to solve the problem of the subjectivity of attribute weighting in TOPSIS. 2. The TOPSIS method just sets up two ideal solutions, namely the positive ideal solution (PIS) and the negative ideal solution (NIS). Its core idea is to find an optimal solution close to the positive ideal solution and far away from the negative ideal solution. However, when the distances between the alternatives and the ideal solution are equal, the TOPSIS method cannot rank the alternatives. In this study, an ideal solution set is designed to solve this limitation of TOPSIS. The improved TOPSIS process flow is as follows:  
Step 1: Establish a multi-attribute decision indicator system. The lines are set as \(U=\left\{u_{1},u_{2},\cdots,u_{m}\right\}\). The decision indicators are set as \(C=\left\{c_{1},c_{2},\cdots c_{n}\right\}\); then, the attribution value set of the lines is set as \(V=\left\{v_{i,j}|i\in\left[1,m\right],j\in\left[1,n\right]\right\}\); the initial decision indicator table is shown in Table 1. It should be noted that the decision indicators are selected in line with factors influencing the characteristics of urban development. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Line**} & \multicolumn{6}{c}{**Indicator**} \\ \cline{2-7}  & \(\mathbf{c_{1}}\) & \(\mathbf{c_{2}}\) & \(\cdots\) & \(\mathbf{c_{j}}\) & \(\cdots\) & \(\mathbf{c_{n}}\) \\ \hline \(u_{1}\) & \(\mathbf{v}_{1,1}\) & \(\mathbf{v}_{1,2}\) & \(\cdots\) & \(\mathbf{v}_{1,j}\) & \(\cdots\) & \(\mathbf{v}_{1,n}\) \\ \(u_{2}\) & \(\mathbf{v}_{2,1}\) & \(\mathbf{v}_{2,2}\) & \(\cdots\) & \(\mathbf{v}_{2,j}\) & \(\cdots\) & \(\mathbf{v}_{2,n}\) \\  
\[DM_{\omega}=\left[