*7.1. Overview*

This section applies the established index system to evaluate the sustainable development of the Harbin-Dalian PDL, a typical HSR project in China. Harbin-Dalian PDL is put into operation by the end of 2012, marking the basic formation of "Four Vertical" in the "Four Vertical and Four Horizontal" of Chinese railway mainline. Harbin-Dalian PDL had finished the connection with existing HSR line of the Beijing-Shanghai and Beijing-Guangzhou. Since the operation of Harbin-Dalian PDL, it has not only shortened the distance of Heilongjiang, Jilin, and Liaoning provinces, but it has also strengthened regional economic integration.

Harbin-Dalian PDL runs through three provinces in Northeast China, 4 sub-provincial cities, and 6 prefecture-level cities. The total length stands at 921 km, including 553 km in Liaoning Province, 270 km in Jilin Province, and 81 km in Heilongjiang Province. Harbin-Dalian PDL starts from Dalian, through Yingkou, Anshan, Liaoyang, Shenyang, Tieling, Siping, Changchun, and Songyuan, and finally to Harbin (see Figure 4). According to the statistics of 2015, the 10 cities account for 40.90% of tourism resources, 46.53% of the population, and 59.87% of the total GDP in Northeast China [55]. Since its opening, the railway has effectively stimulated tourism in the cities along its route and across Northeast China.

**Figure 4.** Images of Harbin-Dalian PDL in China.

Harbin-Dalian PDL is the most advanced technology integration of China's HSR, and its operation has become the most powerful explanation for China's export of "China Railway High-speed" to countries along "the Belt and Road".

Through the investigation and analysis of the HSR construction project, the comprehensive evaluation index can be divided into 5 grades: V = {very poor, poor, qualified, good, excellent}, correspond to V = {v1, v2, v3, v4, v5}. The direct choice of experts is given according to the multi-layered set of factors, and the number of experts supported as judgement of the index. In light of Saaty's 1–9 ratio scale estimation, V = { 1, 3, 5, 7, 9} .

The secondary indices are quantified based on the basic data and expert scoring (by an expert panel consisting of 10 experts in the industry). The single measure vectors of the third indices (See Table 5) are obtained in light of the scores and the membership degree equation.

Thus, according to the vector measures, the measurement matrix of the secondary index is established as follows:


$$\mathbf{I}\_3: \overline{\boldsymbol{\mu}}\_3 = \begin{bmatrix} 0 & 0 & 0 & 0.6 & 0.4 \\ 0 & 0 & 0 & 0.8 & 0.2 \\ 0 & 0 & 0.1 & 0.6 & 0.3 \\ 0 & 0 & 0.2 & 0.6 & 0.2 \\ 0 & 0 & 0.1 & 0.6 & 0.3 \\ 0 & 0 & 0 & 0.5 & 0.5 \\ 0 & 0.1 & 0.2 & 0.6 & 0.1 \\ 0 & 0 & 0.1 & 0.7 & 0.2 \\ 0 & 0 & 0.1 & 0.5 & 0.4 \\ 0 & 0 & 0.1 & 0.5 & 0.4 \\ \end{bmatrix} \\ \mathbf{I}\_4: \overline{\boldsymbol{\mu}}\_4 = \begin{bmatrix} 0 & 0 & 0.1 & 0.7 & 0.2 \\ 0 & 0 & 0 & 0.6 & 0.4 \\ 0 & 0 & 0.1 & 0.6 & 0.3 \\ 0 & 0 & 0 & 0.7 & 0.3 \\ 0 & 0 & 0 & 0.6 & 0.4 \\ 0 & 0 & 0.1 & 0.6 & 0.3 \\ \end{bmatrix}$$

**Table 5.** The weights of hierarchy and expert scoring results.


#### *7.2. Weight Calculation of Second Grade Index*

The weights of the secondary indices are calculated using information entropy. Below is the calculation of weight of process evaluation (F1):

$$\begin{aligned} \mathbf{I}\_1: \mathbb{H}\_1 = \begin{bmatrix} 0 & 0 & 0.2 & 0.5 & 0.3 \\ 0 & 0 & 0.2 & 0.5 & 0.3 \\ 0 & 0 & 0 & 0.5 & 0.5 \\ 0 & 0 & 0 & 0.5 & 0.5 \\ 0 & 0 & 0.1 & 0.5 & 0.4 \\ 0 & 0 & 0 & 0.7 & 0.3 \\ 0 & 0.1 & 0.3 & 0.5 & 0.1 \\ 0 & 0 & 0 & 0.6 & 0.4 \\ 0 & 0 & 0.2 & 0.5 & 0.3 \\ 0 & 0 & 0 & 0.7 & 0.3 \end{bmatrix} \end{aligned}$$

Using Equation (5): v11 = 0.5528, v12 = 0.5528, v13 = 0.6990, v14 = 0.6990, v15 = 0.5903, v16 = 0.7347, v17 = 0.4926, v18 = 0.7077, v19 = 0.5528 and v110 = 0.7347.

Using Equation (6): ω11 = 0.0875, ω12 = 0.0875, ω13 = 0.1107, ω14 = 0.1107, ω15 = 0.0935, ω16 = 0.1163, ω17 = 0.0780, ω18 = 0.1120, ω19 = 0.0875 and ω110 = 0.1163.

Thus, level indices can be obtained under F1 category weights:

> ω1 = (0.0875 0.0875 0.1107 0.1107 0.0935 0.1163 0.0780 0.1120 0.0875 0.1163).

The same way can be obtained under F2, F3, F4 category weights:

ω2 = (0.1692 0.1021 0.2232 0.1692 0.1678 0.1678); ω3 = (0.1131 0.1251 0.0975 0.0938 0.0975 0.1117 0.0842 0.1041 0.0943 0.0787); ω4 = (0.1598 0.1806 0.1442 0.1692 0.1906 0.1806 0.1442).

#### *7.3. Measure Calculation of First Grade Index*

Using Equation (7), the measurement vector of the first index under process evaluation (F1) is:

$$
\boldsymbol{\mu}\_{1} = \overline{\boldsymbol{\mu}}\_{1} \times \overline{\boldsymbol{w}}\_{1} = \begin{bmatrix} 0.0875\\ 0.0875\\ 0.1107\\ 0.1107\\ 0.0935\\ 0.1163\\ 0.0780\\ 0.0780\\ 0.1120\\ 0.0875\\ 0.1163 \end{bmatrix}^{\top} \times \begin{bmatrix} 0 & 0 & 0.2 & 0.5 & 0.3\\ 0 & 0 & 0.2 & 0.5 & 0.3\\ 0 & 0 & 0 & 0.5 & 0.5\\ 0 & 0 & 0 & 0.5 & 0.4\\ 0 & 0 & 0 & 0.7 & 0.3\\ 0 & 0 & 0 & 0.7 & 0.1\\ 0 & 0 & 0 & 0.6 & 0.4\\ 0 & 0 & 0 & 0.6 & 0.4\\ 0 & 0 & 0 & 0.7 & 0.3 \end{bmatrix} = (0.0078\,0.0853\,0.5577\,0.3490)
$$

The measurement vector of the first index under evaluation of economic benefits (F2) is:

$$\begin{aligned} \overline{\mu}\_{2} = \overline{\mu}\_{2} \times \overline{w}\_{2} = \begin{bmatrix} 0.1692 \\ 0.1021 \\ 0.2232 \\ 0.1692 \\ 0.1678 \\ 0.1678 \end{bmatrix}^{\mathrm{T}} \times \begin{bmatrix} 0 & 0 & 0.1 & 0.5 & 0.4 \\ 0 & 0.1 & 0.2 & 0.4 & 0.3 \\ 0 & 0 & 0 & 0.6 & 0.4 \\ 0 & 0.4 & 0.5 & 0.1 & 0 \\ 0 & 0 & 0.2 & 0.6 & 0.2 \\ 0 & 0 & 0.2 & 0.6 & 0.2 \end{bmatrix} = (0.00779 \,0.1890 \,0.4776 \,0.2547) \end{aligned}$$

The measurement vector of the first index under effect evaluation (F3) is:

$$
\boldsymbol{\mu}\_{3} = \overline{\boldsymbol{\mu}}\_{3} \times \overline{\boldsymbol{w}}\_{3} = \begin{bmatrix} 0.1131 \\ 0.1251 \\ 0.0975 \\ 0.0938 \\ 0.0975 \\ 0.1117 \\ 0.0842 \\ 0.1041 \\ 0.0943 \\ 0.0943 \\ 0.0787 \end{bmatrix}^{\top} \times \begin{bmatrix} 0 & 0 & 0 & 0.6 & 0.4 \\ 0 & 0 & 0 & 0.8 & 0.2 \\ 0 & 0 & 0.1 & 0.6 & 0.3 \\ 0 & 0 & 0.2 & 0.6 & 0.3 \\ 0 & 0 & 0 & 0.5 & 0.5 \\ 0 & 0 & 0 & 0.5 & 0.5 \\ 0 & 0 & 0.1 & 0.7 & 0.2 \\ 0 & 0 & 0.1 & 0.5 & 0.4 \\ 0 & 0.1 & 0.1 & 0.5 & 0.3 \end{bmatrix} = (0.0152 \, 0.0828 \, 0.6070 \, 0.3011)
$$

The measurement vector of the first index under sustainability evaluation (F4) is:

$$\mathfrak{u}\_4 = \overline{\mathfrak{u}}\_4 \times \overline{\mathfrak{u}}\_4 = \begin{bmatrix} 0.1598 \\ 0.1806 \\ 0.1442 \\ 0.1906 \\ 0.1806 \\ 0.1442 \end{bmatrix}^T \times \begin{bmatrix} 0 & 0 & 0.1 & 0.7 & 0.2 \\ 0 & 0 & 0 & 0.6 & 0.4 \\ 0 & 0 & 0.1 & 0.6 & 0.3 \\ 0 & 0 & 0 & 0.7 & 0.3 \\ 0 & 0 & 0 & 0.6 & 0.4 \\ 0 & 0 & 0.1 & 0.6 & 0.3 \end{bmatrix} = (0 \ 0 \ 0.0448 \ 0.6350 \ 0.3201)$$

Thus the measurement matrix of the first index is:

$$
\overline{\mathbf{u}} = \begin{bmatrix}
\mu\_1 \\
\mu\_2 \\
\mu\_3 \\
\mu\_4
\end{bmatrix} = \begin{bmatrix}
0 & 0.0078 & 0.0853 & 0.5577 & 0.3490 \\
0 & 0.0779 & 0.1890 & 0.4776 & 0.2547 \\
0 & 0.0152 & 0.0828 & 0.6070 & 0.3011 \\
0 & 0 & 0.0448 & 0.6350 & 0.3201
\end{bmatrix}^T
$$

#### *7.4. Determining the Classification Weight of First Grade Index*

The first index judgment matrix is established using Saaty's 1–9 scale, and AHP is applied to calculate the weights as the final results (see Table 5).

#### *7.5. Calculation of Comprehensive Measure Vector*

Point multiplication of the first index weight and the first measurement matrix results in judgment matrix as follows:

$$\mathbf{B} = \boldsymbol{\omega}\_{\mathbf{i}}^{0} \times \overline{\boldsymbol{\mu}} = \begin{bmatrix} 0.300 \\ 0.339 \\ 0.251 \\ 0.110 \end{bmatrix}^{T} \times \begin{bmatrix} 0 & 0.0078 & 0.0853 & 0.5577 & 0.3490 \\ 0 & 0.0779 & 0.1890 & 0.4776 & 0.2547 \\ 0 & 0.0152 & 0.0828 & 0.6070 & 0.3011 \\ 0 & 0 & 0.0448 & 0.6350 & 0.3201 \end{bmatrix}$$
 
$$= \begin{pmatrix} 0.0326 \ 0.1154 \ 0.5514 \ 0.3018 \end{pmatrix}$$

Thus the score is calculated as:

$$\mathbf{S} = \mathbf{B} \times \mathbf{A} = (0.0.0326 \, 0.1154 \, 0.5514 \, 0.3018) \times (1 \, 3 \, 5 \, 7 \, 9) = 7.2508$$

The calculation results show that the overall score of The Harbin-Dalian PDL is 7.2508, and the sustainable evaluation result is good.

## *7.6. Confidence Level Recognition*

Confidence level recognition is performed using Equation (11) and the calculated comprehensive measurement vector. Here, λ is set as 0.7:

When λ = 0.7, k0 = min k ∑ l=1 μil ≥ 0.7, k = 5; it shows that the confidence level recognition is good.
