# A Novel Variable Weight VIKOR Grade Assessment Method for Waterway Navigation Safe Routes Selection

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## Abstract

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## 1. Introduction

## 2. Description of the Waterway Navigation Safe Route Selection Problems

**Lower bound grade threshold**${B}_{1}$: The eigenvalue ${y}_{ji}$ of alternative ${a}_{j}$ on attribute ${c}_{is}$ is no less than the criterion ${b}_{isk}$ of grade ${e}_{k\text{}}(k=1,2,\cdots ,5)$ on attribute ${c}_{is}$, i.e., ${y}_{jis}\text{}\ge \text{}{b}_{isk}$, which satisfies the condition of ${b}_{is1}\text{}\le \text{}{b}_{is2}\text{}\le \cdots \le \text{}{b}_{is5}$.

**Upper bound grade threshold**${B}_{2}$: The eigenvalue ${y}_{ji}$ of alternative ${a}_{j}$ concerning attribute ${c}_{i\mathrm{s}}$ is no more than the criterion ${b}_{isk}$ of grade ${e}_{k\text{}}(k=1,2,\cdots ,5)$ of attribute ${c}_{is}$, i.e., ${y}_{jis}\text{}\le \text{}{b}_{isk}$, which satisfies the condition of ${b}_{is1}\text{}\ge \text{}{b}_{is2}\text{}\ge \cdots \ge \text{}{b}_{is5}$.

**Linguistic grade threshold**${B}_{3}$: the eigenvalue ${y}_{ji}$ of alternative ${a}_{j}$ on qualitative attribute ${c}_{i\mathrm{s}}$ is linguistic information, i.e.,${y}_{ji}\in {O}_{is}$, where ${O}_{i}=\{{o}_{i1},{o}_{i2},\cdots ,{o}_{i5}\}$ is the grade threshold of the quantitative attribute ${c}_{is}$.

## 3. The Variable Weight VIKOR Assessment Method for the Safety Grade of a Waterway Environment

#### 3.1. The Construction of Membership Function for the Safety Grade of a Waterway Environment

#### 3.2. The Principles and Procedure of the Variable Weight VIKOR Assessment Method

## 4. The Calculation and Analysis of Waterway Navigation Safe Route Selection

#### 4.1. Description of Waterway Navigation Safe Route Selection

#### 4.2. Determination of Waterway Navigation Safe Route Selection

## 5. Conclusions

- (1)
- Security grade division, evaluation index systems and grade thresholds for the navigation waterways of night ships are constructed.
- (2)
- The method to determine the index weight based on entropy and then the variable weight VIKOR method are proposed, the latter of which gives consideration to both group benefits and individual regrets. It not only overcomes the problem that the previous ranking evaluation methods only consider group benefits, but also overcomes the shortcomings that VIKOR method itself only solves the problem of ranking and information compensation among indices. This is an expansion and development of VIKOR methods.
- (3)
- The results of using two-tuple linguistic information to measure the security grade of ships’ night navigation channels reflect the grade information and deviation, judge the security level of each ship’s night navigation waterways, and overcome the shortcomings of the maximum-membership-principle method, and further improve the evaluation method.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Table 1.**The index system and categorisation criterion for assessing the safety grade of a waterway environment.

Indexes | Safety Grade | |||||
---|---|---|---|---|---|---|

${\mathit{e}}_{1}$ | ${\mathit{e}}_{2}$ | ${\mathit{e}}_{3}$ | ${\mathit{e}}_{4}$ | ${\mathit{e}}_{5}$ | ||

Natural factors ${c}_{1}$ | Visibility ${c}_{11}$ | 90 | 50 | 40 | 25 | 15 |

Wind ${c}_{12}$ | 200 | 150 | 100 | 60 | 30 | |

Current velocity ${c}_{13}$ | 7 | 4 | 2.5 | 1.5 | 0.5 | |

Waterway conditions ${c}_{2}$ | Width of waterways ${c}_{21}$ | 0.91 | 0.93 | 0.67 | 0.5 | 0.33 |

Length of waterways ${c}_{22}$ | 0.77 | 0.50 | 0.17 | 0.1 | 0.07 | |

Curvature of waterways ${c}_{23}$ | 90 | 60 | 45 | 30 | 15 | |

Intersection of waterways ${c}_{24}$ | 90 | 70 | 60 | 45 | 20 | |

Obstacles in waterways ${c}_{25}$ | 0.02 | 0.13 | 0.72 | 1.3 | 2.02 | |

Traffic situations ${c}_{3}$ | Traffic volume ${c}_{31}$ | 650 | 500 | 300 | 150 | 70 |

Traffic control ${c}_{32}$ | ${O}_{321}$ | ${O}_{322}$ | ${O}_{323}$ | ${O}_{324}$ | ${O}_{325}$ | |

Navigation aids ${c}_{33}$ | ${O}_{331}$ | ${O}_{332}$ | ${O}_{333}$ | ${O}_{334}$ | ${O}_{335}$ |

Indexes | Routes | ||
---|---|---|---|

${\mathit{a}}_{1}$ | ${\mathit{a}}_{2}$ | ${\mathit{a}}_{3}$ | |

${c}_{11}$ | 28 | 25 | 26 |

${c}_{12}$ | 48 | 42 | 49 |

${c}_{13}$ | 0.8 | 0.6 | 0.7 |

${c}_{21}$ | 0.28 | 0.3 | 0.29 |

${c}_{22}$ | 0.09 | 0.09 | 0.09 |

${c}_{23}$ | 28 | 25 | 35 |

${c}_{24}$ | 47 | 47 | 48 |

${c}_{25}$ | 0.82 | 1.02 | 1.1 |

${c}_{31}$ | 97.4 | 61.6 | 75.6 |

${c}_{32}$ | ${O}_{325}$ | ${O}_{325}$ | ${O}_{325}$ |

${c}_{33}$ | ${O}_{335}$ | ${O}_{335}$ | ${O}_{335}$ |

Routes | The Membership Degree of Safe Rating | Grade Assessment Eigenvalues | Grade Assessment | The Maximum Membership Degree Method | ||||
---|---|---|---|---|---|---|---|---|

${\mathit{e}}_{1}$ | ${\mathit{e}}_{2}$ | ${\mathit{e}}_{3}$ | ${\mathit{e}}_{4}$ | ${\mathit{e}}_{5}$ | ||||

${a}_{1}$ | 0.000 | 0.042 | 0.288 | 0.260 | 0.409 | 4.036 | ${e}_{3}$ | ${e}_{5}$ |

${a}_{2}$ | 0.000 | 0.039 | 0.161 | 0.211 | 0.589 | 4.351 | ${e}_{3}$ | ${e}_{5}$ |

${a}_{3}$ | 0.000 | 0.046 | 0.171 | 0.227 | 0.555 | 4.292 | ${e}_{3}$ | ${e}_{5}$ |

Routes | The Membership Degree of Safe Rating | Grade Assessment Eigenvalues | Grade Assessment | The Maximum Membership Degree Method | ||||
---|---|---|---|---|---|---|---|---|

${\mathit{e}}_{1}$ | ${\mathit{e}}_{2}$ | ${\mathit{e}}_{3}$ | ${\mathit{e}}_{4}$ | ${\mathit{e}}_{5}$ | ||||

${a}_{1}$ | 0.000 | 0.034 | 0.214 | 0.294 | 0.458 | 4.175 | ${e}_{3}$ | ${e}_{5}$ |

${a}_{2}$ | 0.000 | 0.021 | 0.292 | 0.187 | 0.500 | 4.166 | ${e}_{3}$ | ${e}_{5}$ |

${a}_{3}$ | 0.000 | 0.031 | 0.158 | 0.244 | 0.567 | 4.346 | ${e}_{3}$ | ${e}_{5}$ |

Routes | The Membership Degree of Safe Rating of | Grade Assessment Eigenvalues | Grade Assessment | The Maximum Membership Degree Method | ||||
---|---|---|---|---|---|---|---|---|

${\mathit{e}}_{1}$ | ${\mathit{e}}_{2}$ | ${\mathit{e}}_{3}$ | ${\mathit{e}}_{4}$ | ${\mathit{e}}_{5}$ | ||||

${a}_{1}$ | 0.000 | 0.058 | 0.383 | 0.182 | 0.377 | 3.878 | ${e}_{3}$ | ${e}_{3}$ |

${a}_{2}$ | 0.000 | 0.059 | 0.149 | 0.192 | 0.600 | 4.332 | ${e}_{3}$ | ${e}_{5}$ |

${a}_{3}$ | 0.000 | 0.067 | 0.163 | 0.206 | 0.563 | 4.266 | ${e}_{3}$ | ${e}_{5}$ |

Routes | The Membership Degree of Safe Rating of | Grade Assessment Eigenvalues | Grade Assessment | The Maximum Membership Degree | ||||
---|---|---|---|---|---|---|---|---|

${\mathit{e}}_{1}$ | ${\mathit{e}}_{2}$ | ${\mathit{e}}_{3}$ | ${\mathit{e}}_{4}$ | ${\mathit{e}}_{5}$ | ||||

${a}_{1}$ | 0.177 | 0.106 | 0.172 | 0.115 | 0.430 | 3.514 | ${e}_{3}$ | ${e}_{5}$ |

${a}_{2}$ | 0.171 | 0.098 | 0.159 | 0.114 | 0.458 | 3.588 | ${e}_{3}$ | ${e}_{5}$ |

${a}_{3}$ | 0.174 | 0.102 | 0.165 | 0.117 | 0.441 | 3.549 | ${e}_{3}$ | ${e}_{5}$ |

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## Share and Cite

**MDPI and ACS Style**

Yu, G.-F.; Lin, Y.-J.; Luo, X.-M.
A Novel Variable Weight VIKOR Grade Assessment Method for Waterway Navigation Safe Routes Selection. *J. Mar. Sci. Eng.* **2023**, *11*, 347.
https://doi.org/10.3390/jmse11020347

**AMA Style**

Yu G-F, Lin Y-J, Luo X-M.
A Novel Variable Weight VIKOR Grade Assessment Method for Waterway Navigation Safe Routes Selection. *Journal of Marine Science and Engineering*. 2023; 11(2):347.
https://doi.org/10.3390/jmse11020347

**Chicago/Turabian Style**

Yu, Gao-Feng, Yu-Jin Lin, and Xiao-Mei Luo.
2023. "A Novel Variable Weight VIKOR Grade Assessment Method for Waterway Navigation Safe Routes Selection" *Journal of Marine Science and Engineering* 11, no. 2: 347.
https://doi.org/10.3390/jmse11020347