# An Integrated Approach to Risk Assessment for Special Line Shunting Via Fuzzy Theory

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## Abstract

**:**

## 1. Introduction

## 2. Risk Assessment Model

#### 2.1. Context Establishment

#### 2.2. Risk Identification

#### 2.3. Risk Analysis

#### 2.3.1. Fuzzy Reasoning Analysis

_{n}and B

_{n}are the input and output fuzzy sets, x = (x

_{1}, x

_{2}, ..., x

_{n})

^{T}∈ U, y ∈ V, x and y are input and output fuzzy vectors, U and V are the domains of the input and output variables, k = 1, 2, ..., m, and m is the total number of fuzzy rules. Fuzzy rules are determined by expert experience and engineering knowledge; the number of fuzzy rules is determined by the classification of the two inputs of fuzzy reasoning of “likelihood of occurrence” and “severity of consequences.” In this paper, the likelihood of occurrence has six categories of qualitative description, and the severity of consequence has five categories of qualitative description, so thirty fuzzy rules can be established in total. The specific content is shown in Table 4:

_{0}, y

_{0}), according to FRA. To obtain the output language value z

_{0}, the excitation intensity (representing the extent to which the first half of the rule is satisfied) a

_{q}must be determined. a

_{q}can be obtained by the Cartesian product of the fuzzy set sum.

_{0}, y

_{0}) is fuzzified, the membership degree to which x

_{0}belongs to the fuzzy subset A

_{i}is ${u}_{\left({A}_{i}\right)}\left({x}_{0}\right)$, and the membership degree to which y

_{0}belongs to the fuzzy subset B

_{i}is ${u}_{\left({B}_{j}\right)}\left({y}_{0}\right)$, the fuzzy rules that are activated are: “if x is A

_{i}and y is B

_{i}, then z is C

_{k},” and the excitation intensity a

_{q}obtained by fuzzy rules R

_{q}can be obtained by Equation (1):

_{q}, we can use a

_{q}to obtain the MF of C

_{k}, receiving the mapping of the first half to conclusion, and obtain the inference results C

_{k}

^{#}under fuzzy rules R

_{q}, cutting can be expressed by Equation (2). This method is often referred to as the clipping method. See Figure 5 for the FRA process.

_{0}belonging to two different fuzzy sets A

_{i}and A

_{i+1}, besides activating the fuzzy rules R

_{q}, it can also activate other fuzzy rules. Fuzzy aggregation is the process of integrating the mapping results obtained under all activated fuzzy rules. The integrated result represents the output fuzzy set of the whole fuzzy reasoning conclusion, corresponding to the union set of fuzzy relations of each fuzzy rule, as represented by Equation (3) [19]. The process is shown in Figure 6.

_{c}represents the output value of the FRA conclusion. Substituting this value into the initial MF, we can complete the qualitative transformation of fuzzy reasoning results. As can be seen from Figure 7, the membership degree to which the output value belongs to C

_{k}is u(z

_{c1}); that to which it belongs to C

_{k+1}is u(z

_{c2}) [20].

#### 2.3.2. Fuzzy Analytic Hierarchical Process

_{ij}= (l

_{ij}, m

_{ij}, u

_{ij}) where a

_{ij}is the score given by experts on the importance of the item element i relative to the item element j, and l

_{ij}, m

_{ij}, and u

_{ij}are evaluation scales from 1 to 9 satisfying the relationship l

_{ij}≤ m

_{ij}≤ u

_{ij}. l

_{ij}and u

_{ij}respectively represent the minimum and maximum values of the fuzzy range and m

_{ij}is the value considered by experts as the most representative of the relative importance of the two elements [20,21,24]. The meanings expressed by different score ranges are shown in Table 5 and Figure 8.

_{ij}obtained by the experts according to the evaluation scale table.

_{ij}= (l

_{ij}, m

_{ij}, u

_{ij}) should satisfy the following two conditions:

_{p}= (l

_{p}, m

_{p}, u

_{p}) and a

_{q}= (l

_{q}, m

_{q}, u

_{q}), representing two different triangular fuzzy numbers respectively [24,25]. The fuzzy operation rules of the two numbers are as follows:

_{i}is the geometric average of the judgment matrix row i and w

_{i}is the weight of the risk factor i.

_{i}is a fuzzy value, the fuzzy value must be transformed into a non-fuzzy value by defuzzification. In this study, the inverse triangulation fuzzy number formula is adopted [20]. Assuming the triangulation fuzzy number w

_{i}= (l

_{i}, m

_{i}, u

_{i}), the defuzzification calculation formula is as follows:

#### 2.3.3. System Risk

#### 2.4. Risk Evaluation

#### 2.5. Risk Treatment

## 3. Case Application

#### 3.1. Context Establishment

#### 3.2. Risk Identification

#### 3.2.1. Hazard Factor Analysis

#### 3.2.2. Fishbone Diagram

#### 3.2.3. Hierarchical Structure Construction

#### 3.3. Risk Analysis

#### 3.3.1. Risk of Indicator Layer Hazard Factors

#### 3.3.2. Relative Weights of Indicator Layer Hazard Factors

#### 3.3.3. Relative Weights of Hazard Factors in Criterion Layer

#### 3.3.4. System Risk Calculation

#### 3.4. Risk Evaluation

#### 3.5. Risk Treatment

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Railway special-line shunting risk-assessment model. FRA: fuzzy reasoning approach; FAHP: fuzzy analytic hierarchical processing.

Linguistic Term | Estimated Frequency Range | Midpoint of Estimated Frequency | Approximate Numerical Value (Events per year) | MF Parameters |
---|---|---|---|---|

Regular | 1 in 20 days to 1 in 3 months | 1 in 2 months | 6.25 | $\left(1.25,6.25,31.25,31.25\right)$ trapezoid |

Frequent | 1 in 3 months to 1 in 1.75 years | 1 in 9 months | 1.25 | $\left(0.25,1.25,6.25\right)$ triangle |

Occasional | 1 in 1.75 years to 1 in 7 years | 1 in 4 months | 0.25 | $\left(0.05,0.25,1.25\right)$ triangle |

Infrequent | 1 in 7 years to 1 in 35 years | 1 in 20 years | 0.05 | $\left(0.01,0.05,0.25\right)$ triangle |

Rare | 1 in 35 years to 1 in 175 years | 1 in 100 years | 0.01 | $\left(0.002,0.01,0.05\right)$ triangle |

Remote | <175 years | 1 in 500 years | 0.002 | $\left(0,0,0.002,0.01\right)$ trapezoid |

Linguistic Term | Description | Approximate Numerical Value (Event/year) | Parameters of MFs |
---|---|---|---|

Minor | Minor injury | 0.005 | $\left(0,0,0.005,0.025\right)$ trapezoid |

Marginal | Multiple minor injuries | 0.025 | $\left(0.005,0.025,0.125\right)$ triangle |

Moderate | Single serious injury | 0.125 | $\left(0.025,0.125,0.625\right)$ triangle |

Severe | Multiple serious injuries or single fatal injury | 0.625 | $\left(0.125,0.625,3.125\right)$ triangle |

Catastrophic | 2–5 fatal injuries | 3.125 | $\left(0.625,3.125,5,5\right)$ trapezoid |

Risk Category | Description | Risk Scores | Parameters of MF |
---|---|---|---|

Negligible | Risk is acceptable with/without the agreement of the Railway Authority | 0–3 | $\left(0,0,2,3\right)$ trapezoid |

Tolerable | Acceptable with adequate control and with the agreement of the Railway Authority | 2–6 | $\left(2,3,5,6\right)$ trapezoid |

Undesirable | Shall only be accepted when risk reduction is impracticable and with the agreement of the Railway Authority | 5–9 | $\left(5,6,8,9\right)$ trapezoid |

Intolerable | Risk must be reduced in exceptional circumstances | 8–11 | $\left(8,9,11,11\right)$ trapezoid |

Severity of Consequence | Likelihood of Occurrence | |||||
---|---|---|---|---|---|---|

Remote | Rare | Infrequent | Occasional | Frequent | Regular | |

Catastrophic | Tolerable | Undesirable | Undesirable | Undesirable | Intolerable | Intolerable |

Severe | Tolerable | Tolerable | Undesirable | Undesirable | Undesirable | Intolerable |

Moderate | Tolerable | Tolerable | Tolerable | Undesirable | Undesirable | Undesirable |

Marginal | Negligible | Tolerable | Tolerable | Tolerable | Undesirable | Undesirable |

Minor | Negligible | Negligible | Tolerable | Tolerable | Tolerable | Undesirable |

Qualitative Descriptors | Description | Triangular Fuzzy Numbers |
---|---|---|

Same | The two elements are exactly the same | (1, 1, 1) |

Equal importance | The two elements are of equal importance to the shunting event | (1, 1, 2) |

Weak importance | One element is slightly stronger than the other | (2, 3, 4) |

Strong importance | One element is stronger than the other | (4, 5, 6) |

Very strong importance | One element is significantly stronger than the other | (6, 7, 8) |

Absolute importance | One element is definitely stronger than the other | (8, 9, 9) |

Hazard Groups | Hazardous Events | Description |
---|---|---|

Unsafe behavior of personnel | Abnormal psychology | Lack of focus at work, easily distracted, daze phenomenon; constituting violation of personal safety |

Physical defects | High work intensity can cause insomnia, trichomadesis, hypertension, and other ailments that cause production safety accidents | |

Low intellectual quality | The employee’s own cultural level cannot adapt to the job requirements | |

Unsafe condition of equipment | Defect of protective equipment | Inadequate manufacturing strength of protective equipment; workers do not wear protective equipment as required |

Shunting equipment malfunction | Radio damage, rail damage, fastener failure | |

Unsafe protection facilities | Lack of necessary safety facilities | |

Environmental insecurity | Natural disasters | Landslides, debris flows, and other geological disasters |

Poor public security environment | Stolen coal, damaged reinforcements, rail damage | |

Poor working environment | Outdoor operation in hot summers and cold winters can cause occupational disease | |

Defects in management | Imperfect rules and regulations | Rules and regulations are not revised in a timely manner and emergency plans lack practicability |

Safety hazards in the joints | The shunting involves a wide range of aspects and the operation organization is complex, involving a large number of personnel | |

Field operation out of control | Difficult to achieve all-weather monitoring and control of key operation links |

Target Layer | Criterion Layer | Indicator Layer | Likelihood of Occurrence | Severity of Consequence | Risk Score | Risk Category |
---|---|---|---|---|---|---|

Yujialiang coal mine special line shunting risk | Unsafe behavior of personnel R1 | Abnormal psychology R11 | 0.015 | 0.02 | 3.42 | Possible 100% |

Physical defects R12 | 0.01 | 0.03 | 4.00 | Possible 100% | ||

Low intellectual quality R13 | 3.20 | 0.375 | 7.92 | Substantial 100% | ||

Unsafe condition of equipment R2 | Defect of protective equipment R21 | 0.008 | 0.03 | 3.49 | Possible 100% | |

Shunting equipment malfunction R22 | 0.20 | 0.015 | 4.00 | Possible 100% | ||

Defect of protective equipment R23 | 0.20 | 0.01 | 4.00 | Possible 100% | ||

Environmental insecurity R3 | Natural disasters R31 | 0.75 | 0.025 | 5.50 | Possible 50% Substantial 50% | |

Poor public security environment R32 | 1.00 | 0.02 | 6.17 | Substantial 100% | ||

Poor working environment R33 | 0.50 | 0.01 | 4.94 | Substantial 100% | ||

Defects in management R4 | Safety hazards in the joints R41 | 0.10 | 0.015 | 4.00 | Possible 100% | |

Imperfect rules and regulations R42 | 0.01 | 0.02 | 3.42 | Possible 100% | ||

Field operation out of control R43 | 0.60 | 0.10 | 6.10 | Substantial 100% |

Criterion Layer | Unsafe Behavior of Personnel | Unsafe Condition of Equipment | Environmental Insecurity | Defects in Management | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Indicator layer | ${W}_{p}^{1}$ | ${W}_{p}^{2}$ | ${W}_{p}^{3}$ | ${W}_{f}^{1}$ | ${W}_{f}^{2}$ | ${W}_{f}^{3}$ | ${W}_{e}^{1}$ | ${W}_{e}^{2}$ | ${W}_{e}^{3}$ | ${W}_{m}^{1}$ | ${W}_{m}^{2}$ | ${W}_{m}^{3}$ |

Weight | 0.21 | 0.14 | 0.65 | 0.24 | 0.57 | 0.19 | 0.29 | 0.61 | 0.10 | 0.36 | 0.08 | 0.56 |

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**MDPI and ACS Style**

Zhang, H.; Sun, Q.
An Integrated Approach to Risk Assessment for Special Line Shunting Via Fuzzy Theory. *Symmetry* **2018**, *10*, 599.
https://doi.org/10.3390/sym10110599

**AMA Style**

Zhang H, Sun Q.
An Integrated Approach to Risk Assessment for Special Line Shunting Via Fuzzy Theory. *Symmetry*. 2018; 10(11):599.
https://doi.org/10.3390/sym10110599

**Chicago/Turabian Style**

Zhang, Huafeng, and Quanxin Sun.
2018. "An Integrated Approach to Risk Assessment for Special Line Shunting Via Fuzzy Theory" *Symmetry* 10, no. 11: 599.
https://doi.org/10.3390/sym10110599