Taking eight coastal ports in Northeast China as the research object, taking the northeast corn container multimodal transport as the application scenario, and using the hesitation fuzzy multi-attribute decision-making method, this paper constructs the competitiveness evaluation model of each port in attracting corn container supply. According to the evaluation index system shown in Table 1 and the fuzzy interval division standard shown in Table 2, the decision matrix shown in Table 3 is obtained by using the decision matrix construction method.
Table 3
| Dalian Port A | Yingkou Port B | Jinzhou Port C | Beiliang Port D | Dandong Port E | Huludao Port F | Panjin Port G | Suizhong Port H |
X1 | 230 | 2570 | 2300 | 450 | 390 | 622 | 605 | 148 |
X2 | 203 | 200.2 | 201.2 | 199.3 | 205.2 | 202.3 | 203.6 | 202.9 |
X3 | 1.23% | 56.39% | 42.48% | 1.79% | 1.13% | 6.94% | 25% | 13.50% |
X4 | 1700 | 1770 | 3200 | 3400 | 500 | 64 | 50 | 15 |
X5 | 876.50 | 683.30 | 750.30 | 853.10 | 726.20 | 776.30 | 681.60 | 869.70 |
X6 | 2 | 4 | 2 | 2 | 2 | 4 | 4 | 2 |
X7 | 82.5 | 470.5 | 252 | 197 | 150 | 41.2 | 138.8 | 28 |
X8 | 10 | 24 | 8 | 24 | 24 | 50 | 40 | 50 |
X9 | 18 | 13 | 3 | 25 | 21 | 22 | 26 | 12 |
X10 | [6, 7] | [8, 9] | [8, 9] | [7, 8] | [6, 7] | [5, 6] | [5, 6] | [4, 5] |
X11 | [4, 5] | [9, 10] | [8, 9] | [8, 9] | [5, 6] | [5, 6] | [4, 5] | [4, 5] |
X12 | [4, 5] | [8, 9] | [7, 8] | [7, 8] | [5, 6] | [5, 6] | [5, 6] | [4, 5] |
On the basis of constructing the decision matrix, for the benefit type quantitative index, cost type quantitative index and benefit type qualitative index, the formulas (5), (6), (7) and (8) are respectively applied for standardization to obtain the standardized decision matrix as shown in Table 4.
Table 4
Standardized decision matrix
| Dalian Port A | Yingkou Port B | Jinzhou Port C | Beiliang Port D | Dandong Port E | Huludao Port F | Panjin Port G | Suizhong Port H |
X1 | 0.09 | 1.00 | 0.89 | 0.18 | 0.15 | 0.24 | 0.24 | 0.06 |
X2 | 0.98 | 1.00 | 0.99 | 1.00 | 0.97 | 0.99 | 0.98 | 0.98 |
X3 | 0.02 | 1.00 | 0.75 | 0.03 | 0.02 | 0.12 | 0.44 | 0.24 |
X4 | 0.50 | 0.52 | 0.94 | 1.00 | 0.15 | 0.02 | 0.01 | 0.00 |
X5 | 0.78 | 1.00 | 0.91 | 0.80 | 0.94 | 0.88 | 1.00 | 0.78 |
X6 | 0.50 | 1.00 | 0.50 | 0.50 | 0.50 | 1.00 | 1.00 | 0.50 |
X7 | 0.18 | 1.00 | 0.54 | 0.42 | 0.32 | 0.09 | 0.30 | 0.06 |
X8 | 0.20 | 0.48 | 0.16 | 0.48 | 0.48 | 1.00 | 0.80 | 1.00 |
X9 | 0.69 | 0.50 | 0.12 | 0.96 | 0.81 | 0.85 | 1.00 | 0.46 |
X10 | [0.29,0.39] | [0.39,0.51] | [0.39,0.51] | [0.34,0.45] | [0.29,0.39] | [0.24,0.34] | [0.24,0.34] | [0.19,0.28] |
X11 | [0.19,0.28] | [0.44,0.56] | [0.39,0.51] | [0.39,0.51] | [0.24,0.34] | [0.24,0.34] | [0.19,0.28] | [0.19,0.28] |
X12 | [0.19,0.28] | [0.39,0.51] | [0.34,0.45] | [0.34,0.45] | [0.24,0.34] | [0.24,0.34] | [0.24,0.34] | [0.19,0.28] |
According to definition 1, the index weight in the port competitiveness evaluation model is solved by using the concept of interval distance, and the single objective optimization model as shown below is constructed according to formulas (1), (2), (3) and (9).
MaxD(w) = 10.96w1 + 14w2 + 11.6w3 + 11.26w4 + 13.37w5 + 13.63w6 + 10.97w7 + 13.43w8 + 12.4w9 + 5.24w10 + 6.29w11 + 5.64w12
s.t.0.08 ≤ w1 ≤ 0.16, 0.06 ≤ w2 ≤ 0.14, 0.07 ≤ w3 ≤ 0.15, 0.10 ≤ w4 ≤ 0.16, 0.08 ≤ w5 ≤ 0.14, 0.06 ≤ w6 ≤ 0.14, 0.08 ≤ w7 ≤ 0.16, 0.08 ≤ w8 ≤ 0.14, 0.08 ≤ w9 ≤ 0.12, 0.07 ≤ w10 ≤ 0.12, 0.08 ≤ w11 ≤ 0.16, 0.06 ≤ w12 ≤ 0.14
\(\sum\limits_{{i=1}}^{{12}} {{w_i}=1,} {\text{ }}{w_i} \geqslant 0,{\text{ }}i \in (1,2,3,...12)\)
Using Python 2.7 software to solve the model, the optimal weight vector is
w=(0.08,0.14,0.07,0.1,0.08,0.08,0.08, 0.08, 0.08, 0.07, 0.08, 0.06)
According to formula 10, the comprehensive index value \({z_j}(w)(j \in N)\) is
zA(w)=[0.4315,0.4508],zB(w)=[0.7454,0.7706],zC(w)=[0.6136,0.6378],zD(w)=[0.5845,0.6081],zE(w)=[0.4624,0.4828],zF(w)=[0.5239,0.5437],zG(w)=[0.5633,0.5825],zH(w)=[0.4246,0.4429],
According to formula (4), calculate the possibility of comparing the comprehensive index values of port competitiveness, and establish the possibility matrix.
\(p=\left\{ {\begin{array}{*{20}{c}} {0.5}&0&0&0&0&0&0&{0.6975} \\ 1&{0.5}&1&1&1&1&1&1 \\ 1&0&{0.5}&1&1&1&1&1 \\ 1&0&0&{0.5}&1&1&1&1 \\ 1&0&0&0&{0.5}&0&0&1 \\ 1&0&0&0&1&{0.5}&0&1 \\ 1&0&0&0&1&1&{0.5}&1 \\ {0.3025}&0&0&0&0&0&0&{0.5} \end{array}} \right\}\)
According to the formula 11, the order vector of probability p is
h=(0.075,0.1875,0.1696,0.1518,0.0982,0.1161,0.1339,0.0679)
The right ordering vector h and the possibility degree in proof P are obtained, and the ordering of interval number \({z_j}(w)\) is
ZB(w)\(\mathop \geqslant \limits_{1}\)ZC(w)\(\mathop \geqslant \limits_{1}\)ZD(w)\(\mathop \geqslant \limits_{1}\)ZG(w)\(\mathop \geqslant \limits_{1}\)ZF(w)\(\mathop \geqslant \limits_{1}\)ZE(w)\(\mathop \geqslant \limits_{1}\)ZA(w)\(\mathop \geqslant \limits_{{0.6975}}\)ZH(w)
It shows that Yingkou Port ranks the highest in the competitiveness of corn container multimodal transport in Northeast China among Liaoning ports, followed by Jinzhou port, Beiliang port, Panjin Port, Huludao port and Dandong port, and the advantage probability reaches 100%. Dalian port is superior to Suizhong port by nearly 70%, ranking seventh and Suizhong port eighth. Due to national policy guidance, enterprise strategic planning of Liaogang group and market demand, Dalian port is inferior in the supply competition of corn container transportation market in Northeast China, while Yingkou Port has obvious advantages in hinterland distance, transportation price, service maturity and awareness.