A risk evaluation model for channel navigation based on the gray-fuzzy theory
- Yanfeng Wang^{1, 2, 3}Email author,
- Liwen Huang^{1, 2},
- Guohua Shen^{3} and
- Mingming Jia^{1, 4}
https://doi.org/10.1186/s13638-018-1159-5
© The Author(s). 2018
Received: 12 February 2018
Accepted: 30 May 2018
Published: 15 June 2018
Abstract
In view of the fuzziness and randomness of the safety evaluation of the channel navigation environment, a risk evaluation model of the channel navigation is established with the set-valued statistics and the gray theory. A safety evaluation index system of channel navigation consisting of first-level indexes for the natural environment, navigation conditions, and traffic environment as well as 12 s-level indexes were established on the basis of comprehensively analyzing factors influencing the safety of the channel navigation environment. The weight of each evaluation index is determined through the model utilizing the set-valued statistics; also, the evaluation sample matrix is determined to realize the initial construction of the environmental scenario of channel navigation; and the safety of the channel navigation environment is evaluated quantitatively with the gray fuzzy comprehensive evaluation method. Taking Guangdong inland channel as an example, the result shows that the safety evaluation method based on the set-valued statistics and the gray fuzzy theory features simple calculation as well as objective and accurate results, which is convenient for practical application.
Keywords
1 Introduction
The channel is an important part of the water transport system, whose navigation environment has a significant impact on the safe navigation of the ship. Frequent accidents of channel navigation have not only caused great losses to the country, but also hindered the sustainable development of channels. How to protect the safety of shipping navigation environment is an important research work on safety management of shipping channel. There are many factors affecting the safety of the channel navigation environment. In order to ensure the safety of channel navigation, these influencing factors should be analyzed and studied to provide a scientific and reasonable judging basis for the safety evaluation of the channel navigation environment.
A variety of research have been made on the channel navigation environment by many professionals. Wang et al. [1] not only proposed a DEA model algorithm, but also analyzed and evaluated navigation environments in channels of Keelung and Kaohsiung, etc. through using linear programming and data envelopment analysis. WANG Jie et al. [2] conducted a comprehensive study of channel navigation environment via adopting the set pair method upon analyzing channel conditions, hydrological weather, traffic, navigation supports and port supports, etc. By constructing a potential risk evaluation model, Park Y S et al. [3] carried out risk evaluations of ships navigating around South Korea’s coast to achieve a scientific evaluation of navigation risk of the inbound navigation channel in Busan. Pietrzykowski Z et al. [4] evaluated the navigation risks in restricted waters with the electronic chart system, so as to provide decision-making for ship navigation. Xiao X et al. [5] evaluated the navigation risks in the unknown environment based on the comprehensive safety evaluation method. Zaman et al. [6] achieved risk evaluation in the navigation channels using the comprehensive safety evaluation method with the accident-prone Malacca Strait as a research object. P.Tmcoo et al. [7] quantitatively evaluated risks of human factors with the use of Bayesian evaluation model in order to obtain objective and authentic evaluation results.
Due to the fuzziness and randomness of the safety evaluation of navigation in the channel environment, only using traditional evaluation methods may easily cause inaccurate results due to strong subjectivity. JIA Jinzhang et al. [8] has utilized the set-valued statistics to determine the weight of external fire evaluation indicators of coal mines, effectively reducing the impact of subjective factors on the evaluation results. Arasteh A et al. [9] studied the project portfolio based on the gray theory and the fuzzy theory to prove that the proposed methods are convenient and practical upon case study. Singh R et al. [10] introduced a fuzzy and gray combining algorithm to study the possible risk of failure in the distribution system; the algorithm is proved to be beneficial to the management of distribution system. Goyal S et al. [11] ranked advantages and disadvantages of advanced manufacturing systems to help managers choose the best manufacturing system with the use of the fuzzy-gray relation.
In order to reduce the uncertainty and subjectivity in determining the weights of the safety evaluation indexes of channel navigation as well as to obtain objective and accurate evaluation results, a gray fuzzy evaluation model is established in this paper through combining the set-valued statistics method with the gray fuzzy theory, which aims at providing research methods for managing the channel safety.
2 Establish a navigation risk evaluation index system
Index factors for risks of channel navigation
No. | Index factor | No. | Index factor | No. | Index factor |
---|---|---|---|---|---|
X _{1} | Wind | X _{8} | Width of channel | X _{15} | Traffic flow |
X _{2} | Wave | X _{9} | Length of channel | X _{16} | Maritime control |
X _{3} | Current | X _{10} | Channel bending | X _{17} | Navigation facilities |
X _{4} | Tide | X _{11} | Obstruction | X _{18} | Management system |
X _{5} | Visibility | X _{12} | Hydraulic structure | X _{19} | VTS coverage |
X _{6} | Precipitation | X _{13} | Turning point | X _{20} | Salvage from the shore |
X _{7} | Depth of channel | X _{14} | Channel intersection |
The safety index system in the inland channel navigating environment
First-level evaluation factor | Second-level evaluation factor |
---|---|
Natural environment Y_{1} | Wind X_{1} |
Current X_{3} | |
Visibility X_{5} | |
channel environment Y_{2} | Depth of channel X_{7} |
Width of channel X_{8} | |
Channel bending X_{10} | |
Obstruction X_{11} | |
Turning point X_{13} | |
Channel intersection X_{14} | |
Traffic environment Y_{3} | Traffic flow X_{15} |
Navigation facilities X_{17} | |
VTS coverage X_{19} |
3 Determine weights of evaluation indexes
Determining the weight of risk evaluation of channel navigation is an important process for evaluating the research object. At the same time, whether the weight determined is reasonable has a direct impact on the accuracy of the final evaluation results. Many scholars have studied calculation methods of index weights from both subjective and objective perspectives. After referring to related literature and comparatively analyzing weight calculation methods, two commonly used methods at present are AHP and entropy weight. Of which, AHP mainly calculates the index weight of evaluation with human’s subjective experience, while the entropy weight calculates the index weight of evaluation through correlation analysis of data. It is difficult to obtain accurate index weights via using traditional weight calculation methods due to the complexity of channel navigation environment. Hence, a method of set-valued statistics is adopted in this paper to determine index weights. The method of set-valued statistics is a fuzzy interval instead of a definite value in the classical statistics, which can accurately reflect experts’ scoring criteria and increase the credibility of evaluation results. Therefore, the set-valued statistics is adopted in this paper to determine the weight of each index of evaluation.
3.1 Determine the weight with set-valued statistics
According to the principle of set-valued statistics, the weight of the evaluation index can be determined. In a certain evaluation index system, the evaluation index is set as m, its set composed is
C = {C_{1}, C_{2}, ..., C_{m}}. Supposing there are n experts involved in judging indexes, the set composed is
Estimated interval of the weight of the evaluation index
Evaluation expert | Evaluation index security range | |||||
---|---|---|---|---|---|---|
C _{1} | C _{2} | … | C _{ i } | … | C _{ m } | |
p _{1} | [a_{11},b_{11}] | [a_{12},b_{12}] | … | [a_{1i},b_{1i}] | … | [a_{1m},b_{1m}] |
p _{2} | [a_{21},b_{21}] | [a_{22},b_{22}] | … | [a_{2i},b_{2i}] | … | [a_{2m},b_{2m}] |
… | … | … | … | … | … | … |
p _{ k } | [a_{k1},b_{k1}] | [a_{k2},b_{k2}] | … | [a_{ ki },b_{ ki }] | … | [a_{ km },b_{ km }] |
… | … | … | … | … | … | … |
p _{ n } | [a_{n1},b_{n1}] | [a_{n2},b_{n2}] | … | [a_{ ni },b_{ ni }] | … | [a_{ nm },b_{ nm }] |
3.2 Reliability analysis of index weight
The larger the Fi, the lower the reliability of the weight of the evaluation index is indicated; the smaller the Fi, the higher the reliability of the weight of the evaluation index is indicated.
4 Methods section
The gray-fuzzy evaluation model is an evaluation model based on the gray system theory and the fuzzy mathematics theory. At present, the model is widely used in risk evaluation, effectively resolving a series of ambiguities and uncertainties. In view of the fuzziness and uncertainty of the channel navigation system, a gray-fuzzy risk evaluation model of channel navigation is built in this chapter on the basis of the gray system theory and the fuzzy mathematics theory, so that theoretical supports can be provided for evaluating the risk of navigation channel and ensuring the navigation safety of that channel.
4.1 The gray system theory
As a core of the gray system theory, the whitening weight function is an important step in the gray research. At present, there are three common types of whitening weight functions, i.e., upper-level, intermediate, and lower-level; specific shape functions and expressions are presented as follows:
4.2 Construct a gray-fuzzy evaluation model
A channel navigation risk evaluation model is established according to the above gray-fuzzy evaluation model. Steps of model building are presented as follows:
4.2.1 (1) Construct a sample matrix
According to the determined navigation risk evaluation index system [21, 22], a risk evaluation model channel navigation is constructed. The gray-fuzzy evaluation method is used to evaluate the safety evaluation for the evaluation index C. The set of first-level evaluation indexes is set as C = {C_{1}, C_{2}, ..., C_{i}, ..., C_{s}}; where, i = 1, 2, ..., s. The set of second-level evaluation indexes is C_{i} = {C_{i1}, C_{i2}, ..., C_{ij}, ..., C_{it}} (t is the number belonging to the first-level evaluation indexes in the second-level evaluation indexes); where, j = 1, 2, ..., t.
4.2.2 (2) Establish a whitening weight function
Threshold corresponding to each gray class
Gray class | e = 1 | e = 2 | e = 3 | e = 4 | e = 5 |
Threshold | 1 | 3 | 5 | 7 | 9 |
4.2.3 (3) Construct a second-level gray-fuzzy evaluation matrix
4.2.4 (4) Calculate first-level index evaluation results
When calculating evaluation results of the first-level evaluation indexes, each weight W_{i} = (w_{i1}, w_{i2}, ..., w_{ij}, ..., w_{it}) of the second-level evaluation indexes multiplied by the corresponding second-level gray-fuzzy evaluation matrix r_{i}, respectively, can obtain the corresponding evaluation results os first-level indexes, i.e., R_{i} = W_{iri}.
4.2.5 (5) Calculate the comprehensive evaluation result
The calculation method of the evaluation result of the first- level index C_{i} is utilized to obtain the final evaluation result R of the total target C, i.e., R = Wr. According to the principle of maximum membership degree, the maximum value of the evaluation result R is obtained in C, whose corresponding gray class is the comprehensive evaluation result.
5 Experimental section
Parameters of navigation in the Guangdong inland channel
Index factor | Channel parameters |
---|---|
Wind | 0.3948 m/s |
Current | 0.0943 m/s |
Width of channel | 160 m |
Length of channel | 8596 m |
Turning point V | V-29° |
Turning point U | U-21° |
Coverage of the navigation aid facility | 90% |
5.1 Determination of evaluation index weights
Evaluation index security range
Evaluation expert | Evaluation expert weight | Evaluation index security range | ||
---|---|---|---|---|
Y _{1} | Y _{2} | Y _{3} | ||
P _{1} | 0.2 | [2.9,4.1] | [7.4,7.7] | [2.8,3.4] |
P _{2} | 0.15 | [3.1,3.6] | [6.7,7.4] | [2.1,2.5] |
P _{3} | 0.25 | [3.6,4.1] | [6.2,7.1] | [2.4,2.7] |
P _{4} | 0.30 | [4.2,4.5] | [7.0,7.1] | [2.6,3.1] |
P _{5} | 0.10 | [4.4,4.8] | [6.9,7.1] | [3.0,3.5] |
According to the Eq. (9), the relative weight \( \overline{w} \) = (3.61, 7.02, 2.16) of first-level indexes including natural environment, channel condition, and traffic environment are calculated. With the Eq. (10), the relative weight solved is processed in normalization to determine the final weight of the three first-level indexes W = (0.274, 0.501, 0.212).
Likewise, weights of all kinds of second-level indexes in the index system can be also solved. Calculated results of weight calculation for all kinds of second-level indexes are W_{1} = (0.231, 0.452, 0.281), W_{2} = (0.156, 0.212, 0.131, 0.120, 0.171, 0.157), and W_{3} = (0.271, 0.414, 0.312), respectively.
It is necessary to test the index weights solved in order to determine whether the weight is reasonable. Also, the reliability of index weight can be tested according to the interval variance method; where, F = (0.253, 0.121, 0.124). The test results show that the reliability of the index weight of the traffic environment is relatively high, while the natural environment index is relatively low.
5.2 Determine the evaluation sample matrix
On the basis of calculating the weight of the index, the evaluation model is used for calculating and analyzing the risk of channel navigation [25]. Experts are invited to score second-level indexes and to establish a scoring standard with a scoring range of [0,10]. Each expert score evaluation indexes and count scores based on the actual situation of the inland channel. Based on the above research results, analyzing steps for conducting navigation risk evaluation in the research are presented as follows:
5.2.1 (1) Determine the evaluation coefficient in the evaluation of gray class
For the second-level index X_{1}, when e = 1 according to the Eq. (24),
y_{111} = f _{1}(d_{111}) + f _{1}(d_{112}) + … + f _{1}(d_{11n}) = 37.136.
Similarly, when e = 2, y112 = 47.766; when e = 3, y113 = 66.880; when e = 4, y114 = 77.950; and when e = 5, y115 = 60.614. On the basis of Eqs. ((25) and (26), the evaluation coefficient corresponding to each evaluation gray class is further calculated and normalized to calculate the weight vector of gray evaluation,
r_{11} = (0.117,0.161,0.232,0.168,0.210)
and X_{5} are calculated respectively as
r_{12} = (0.071, 0.138, 0.213, 0.351, 0.222)
r_{13} = (0.091, 0.114, 0.136, 0.233, 0.416).
5.2.2 (2) Determine the gray-fuzzy evaluation matrix
According to the obtained gray evaluation vector, the gray-fuzzy evaluation matrix is established as
5.2.3 (3) Determine evaluation results of first-level indicating evaluation
According to the method of calculating first-level index evaluation results, the first-level evaluation index evaluation results R_{i} = W_{iri} are obtained as
R_{1} = (0.091,0.132,0.193,0.287,0.281)
R_{2} = (0.125,0.173,0.240,0.252,0.187)
R_{3} = (0.115,0.142,0.218,0.243,0.256).
5.3 Calculation and analysis of evaluation results of the comprehensive system model
According to the evaluation results of first-level indexes, a comprehensive gray-fuzzy evaluation matrix is established. According to the method of calculating results of first-level index evaluation, the final evaluation result of the channel can be obtained as
R = W r = (0.113,0.154,0.210,0.270,0.232).
The maximal value in the comprehensive evaluation result of channel safety in the inland channel in Guangdong is β_{4} = 0.252. In that case, the gray class of the evaluation results obtained is 4 according to the principle of maximum membership degree in the fuzzy theory, which indicates that the navigation environment of the channel is “relatively safe.”
6 Conclusions
The set-valued statistics is combined with the gray-fuzzy theory in this paper. The set-valued statistics is utilized to determine the index weight of the navigation system of the inland channel, reducing the influence of subjective factors on the evaluation results of the inland channel; also, the gray-fuzzy theory is utilized to quantitatively process the evaluation indexes, achieving the evaluation indexes transforming from qualitatively to quantitatively. Finally, an environmental safety evaluation model of navigation channel based on the set-valued statistics and the gray-fuzzy theory has been established. Moreover, the evaluation system model was adopted to calculate and analyze the environmental safety of navigation in the inland channel in Guangdong. The evaluation result obtained was relatively safe, being consistent with the actual situation. Besides, the method is highly operable in practical applications due to its objective and accurate evaluation results in comparison to traditional evaluation methods.
Declarations
Acknowledgements
The research presented in this paper was supported by the Natural Science Foundation of China, and Research and Innovation Team of WTCC.
Funding
The authors acknowledge the Natural Science Foundation of China “Research on Mechanism of Ship-Entropy Catastrophe Response to Seafarer-Ship-Environment Disadjust” (51379170), Research and Innovation Team of WTCC(CX2018A04).
Availability of data and materials
The simulation code can be downloaded at Guangdong Maritime Safety Administration.
Authors’ contributions
WYF is the main writer of this paper. He proposed the main idea, deduced the a risk evaluation model of the channel navigation, completed the simulation, and analyzed the result. HLW introduced the set-valued statistics and the gray theory. JMM collected data about the channel in Guangdong Province. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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