# An IT2FS-ANP- and IT2FS-CM-Based Approach for Conducting Safety Risk Assessments of Nuclear Power Plant Building Projects

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motivation

#### 1.2. Literature Review

#### 1.3. Research Objective and Novel Contributions

## 2. Materials and Methods

#### 2.1. Definitions of the IT2FS-ANP and IT2FS-CM Methods

#### 2.1.1. IT2FS

**Definition**

**1.**

_{a}is the primary membership function; b is a secondary factor; and ${\mu}_{\stackrel{\approx}{T}}(a,b)$ is a secondary membership function.

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

**Definition**

**5.**

#### 2.1.2. IT2FS-ANP

**Definition**

**6.**

_{ij}denotes the relative importance of the assessment indexes U

_{i}and U

_{j}; n is the number of assessed indexes.

#### 2.1.3. IT2FS-CM

**Definition**

**8.**

**Definition**

**9.**

**Definition**

**10.**

_{i}($\underset{\xaf}{E{x}_{i}}$, $\overline{E{x}_{i}}$, En

_{i}, He

_{i}) is calculated as follows:

#### 2.2. The IT2FS-ANP- and IT2FS-CM-Based Approach

#### 2.2.1. Theoretical Framework

#### 2.2.2. Stages of SRA

_{b}(Ex

_{b}, En

_{b}, He

_{b}) for the SRA comprises five assessment level clouds, including outstanding, good, moderate, general, and unsatisfactory levels for NPPBPs in China. The outstanding and unsatisfactory assessment level clouds are one-sided constraints, the numerical features of which are defined by Equations (18) and (19). The three remaining assessment level clouds are two-sided constraints, and their numerical features are defined by Equation (20) [97]:

_{min}and s

_{max}represent the minimum bound and maximum bound of the assessment index value, respectively; k is a constant, the value of which is determined according to the fuzzy threshold of the variable itself. In this paper, k takes 0.1.

_{i}($\underset{\xaf}{E{x}_{i}}$, $\overline{E{x}_{i}}$, En

_{i}, He

_{i}) for the SRA were defined as follows:

_{0}($\underset{\xaf}{E{x}_{0}}$, $\overline{E{x}_{0}}$, $E{n}_{0}$, $H{e}_{0}$) for the SRA were defined as follows, with the use of Step 3 from Stage 2:

_{i}is the i-th weight of the assessment index.

- (1)
- Use En
_{0}as the mathematical expectation and He_{0}as the standard deviation in a normal distribution and calculate the normal random number y_{i}. - (2)
- Use $\frac{\underset{\xaf}{E{x}_{0}}+\overline{E{x}_{0}}}{2}$ as the mathematical expectation and y
_{i}as the standard deviation in a normal distribution and calculate the normal random number a_{i}. - (3)
- Calculate $u({a}_{i})=\mathrm{exp}\left[-\frac{{({a}_{i}-\frac{\underset{\xaf}{E{x}_{0}}+\overline{E{x}_{0}}}{2})}^{2}}{2{y}_{i}^{2}}\right]$.
- (4)
- Repeat the above procedures (1)–(3) until N cloud droplets are generated.

_{0}($\underset{\xaf}{E{x}_{0}}$, $\overline{E{x}_{0}}$, $E{n}_{0}$, $H{e}_{0}$), index cloud C

_{i}($\underset{\xaf}{E{x}_{i}}$, $\overline{E{x}_{i}}$, $E{n}_{i}$, $H{e}_{i}$), and number N of cloud droplets.

- (1)
- Use $\frac{\underset{\xaf}{E{x}_{i}}+\overline{E{x}_{i}}}{2}$ as the mathematical expectation and $H{e}_{i}^{2}$ as the variance in a normal distribution to calculate the normal random number z
_{j}. - (2)
- Use $\frac{\underset{\xaf}{E{x}_{0}}+\overline{E{x}_{0}}}{2}$ as the mathematical expectation and ${z}_{j}^{2}$ as the variance in a normal distribution to calculate the normal random number k
_{j}. - (3)
- Calculate ${u}_{j}^{\prime}=\mathrm{exp}\left[\frac{-{({k}_{j}-E{x}_{i})}^{2}}{2{(E{n}_{i})}^{2}}\right]$.
- (4)
- Repeat the above procedures until N cloud droplets are generated.
- (5)
- Use $\varphi =\frac{1}{n}{\displaystyle \sum _{j=1}^{n}{u}_{j}^{\prime}}$ to calculate the similarity between the overall cloud and the outstanding level cloud.

## 3. Application of the Approach

#### 3.1. Case Description

#### 3.2. Conducting the SRA

_{1}. The safety risk was taken as the first rule and the assessment index U

_{11}as the second rule for the NPPBP; the importance was pairwise compared between the four second assessment indexes in the first assessment index U

_{1}, and its IT2F JM was constructed, as shown in Table 3.

## 4. Results and Discussion

#### 4.1. Comparison to the Traditional Method

- (1)
- The IT2FS-ANP method was compared with the traditional ANP method.

- (2)
- The IT2FS-CM method was compared with the traditional CM method.

#### 4.2. Analysis of Assessment Results

_{4}) has a positive influence on occupational health (U

_{1}). This means that good organizational management positively promotes reductions in risks to occupational health. By the same token, highly effective occupational health and safety management systems (U

_{41}) can help to identify, assess, and control occupational health and safety hazards (U

_{42}). This is a highly important discovery because none of these risks are independent, and each is influenced by other risks. Therefore, it is necessary to use the system engineering principle to scientifically manage them [102].

_{21}, U

_{24}, U

_{31}, U

_{32}, and U

_{41}were assessed at Level I (outstanding), and the others were assessed at Level II (good). The results demonstrate that, although the safety risk level was assessed at Level I (i.e., safety risk management was outstanding) for the NPPBP in LXNPCL, there were still deficiencies in safety risk management according to the assessment index, which was assessed at Level II. In response to the safety risk ranking, LXNPCL took positive actions and formulated modified measures in turn, and its safety risk management was improved.

#### 4.3. Analysis of Assessment Results

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Theoretical framework of the IT2FS-ANP- and IT2FS-CM-based approach for the SRA of NPPBPs.

**Figure 4.**Overall cloud and SC for the SRA of the NPPBP in LXNPCL. Notes: the horizontal coordinate represents the standard assessment value, and the vertical coordinate represents the membership level; blue cloud droplets represent the overall cloud, and red cloud droplets show the SC for the SRA.

Linguistic Scales for Importance | Trapezoidal IT2FS |
---|---|

Equally important | (1, 1, 1, 1; 1, 1), (1, 1, 1, 1; 1, 1) |

Slightly more important | (1, 2, 4, 5; 1, 1), (1.2, 2.2, 3.8, 4.8; 0.8, 0.8) |

Strongly more important | (3, 4, 6, 7; 1, 1), (3.2, 4.2, 5.8, 6.8; 0.8, 0.8) |

Very strongly more important | (5, 6, 8, 9; 1, 1), (5.2, 6.2, 7.8, 8.8; 0.8, 0.8) |

Absolutely more important | (7, 8, 9, 9; 1, 1), (7.2, 8.2, 8.8, 9; 0.8, 0.8) |

**Table 2.**Index system for the SRA (Xu et al. [101]).

No. | First Level Index | Second Level Index |
---|---|---|

1 | Occupational health (U_{1}) | Physical health status (U_{11}) |

2 | Mental health status (U_{12}) | |

3 | Occupational risk (U_{13}) | |

4 | Safety protection (U_{2}) | Safety protection facility (U_{21}) |

5 | Personal protective equipment (U_{22}) | |

6 | Safety mark (U_{23}) | |

7 | Material, machinery, and equipment (U_{3}) | Quality of material, machinery, and equipment (U_{31}) |

8 | Installation and dismantling of machinery and equipment (U_{32}) | |

9 | Maintenance of machinery and equipment (U_{33}) | |

10 | Organizational management (U_{4}) | Establishment of safety management system (U_{41}) |

11 | Safety hazard identification, risk assessment, and control (U_{42}) | |

12 | Education and training (U_{43}) | |

13 | Emergency disposal and rescue (U_{44}) |

**Table 3.**IT2F JM for the pairwise comparison of importance between the three second assessment indexes in first assessment index U

_{1}.

Index | U_{11} | U_{12} | U_{13} |
---|---|---|---|

U_{11} | 1 | (1/9, 1/8, 1/6, 1/5; 1, 1) (1/8.8, 1/7.8, 1/6.2, 1/5.2; 0.8, 0.8) | (5, 6, 8, 9; 1, 1), (5.2, 6.2, 7.8, 8.8; 0.8, 0.8) |

U_{12} | (5, 6, 8, 9; 1, 1), (5.2, 6.2, 7.8, 8.8; 0.8, 0.8) | 1 | (1/9, 1/9, 1/8, 1/7; 1, 1) (1/9, 1/8.8, 1/8.2, 1/7.2; 0.8, 0.8) |

U_{13} | (1/9, 1/8, 1/6, 1/5; 1, 1) (1/8.8, 1/7.8, 1/6.2, 1/5.2; 0.8, 0.8) | (7, 8, 9, 9; 1, 1), (7.2, 8.2, 8.8, 9; 0.8, 0.8) | 1 |

Non-Normalized IT2F Weight Vector | Non-Normalized Weight Vector | Improved Normalized Weight Vector |
---|---|---|

(0.8221, 0.9086, 1.1006, 1.2164; 1, 1) (0.8392, 0.9263, 1.0795, 1.1917; 0.8, 0.8) | 0.9604 | 0.3341 |

(0.8221, 0.8736, 1, 1.0874; 1, 1) (0.8329, 0.8898, 0.9835, 1.0692; 0.8, 0.8) | 0.8980 | 0.3124 |

(0.9196, 1, 1.1447, 1.2164; 1, 1) (0.9353, 1.0168, 1.1238, 1.2006; 0.8, 0.8) | 1.0162 | 0.3535 |

Assessment Level | Value Interval | Numerical Feature |
---|---|---|

Outstanding (I) | [90, 100] | (100, 3.333, 0.1) |

Good (II) | [80, 90] | (85, 1.667, 0.1) |

Moderate (III) | [70, 80] | (75, 1.667, 0.1) |

General (IV) | [60, 70] | (65, 1.667, 0.1) |

Unsatisfactory (V) | [0, 60] | (0, 20, 0.1) |

**Table 6.**Numerical features, assessment level, similarity, and risk ranking for the assessment indexes for the SRA of the NPPBP in LXNPCL.

No. | Assessment Index | Numerical Feature | Assessment Level | Similarity | Risk Ranking |
---|---|---|---|---|---|

1 | U_{11} | (87.9, 91.8, 1.2533, 0.1235) | II | 0.9087 | 1 |

2 | U_{12} | (83.1, 88.2, 3.8602, 1.0268) | II | 0.5026 | 8 |

3 | U_{13} | (83.7, 88.7, 6.0159, 1.1681) | II | 0.3611 | 11 |

4 | U_{14} | (87.9, 92.0, 2.8074, 0.7576) | II | 0.7273 | 5 |

5 | U_{21} | (91.4, 95.3, 2.0053, 0.1523) | I | 0.4099 | 10 |

6 | U_{22} | (86.3, 90.2, 1.8800, 0.9898) | II | 0.7732 | 3 |

7 | U_{23} | (85.4, 89.9, 2.6320, 0.6795) | II | 0.7333 | 4 |

8 | U_{24} | (87.6, 92.5, 2.3562, 0.5200) | I | 0.7958 | 2 |

9 | U_{31} | (89.7, 93.6, 2.2560, 0.7677) | I | 0.6234 | 6 |

10 | U_{32} | (91.8, 95.6, 1.4037, 0.3043) | I | 0.3577 | 12 |

11 | U_{33} | (83.1, 88.1, 2.0053, 0.4483) | II | 0.4608 | 9 |

12 | U_{41} | (92.0, 95.8, 1.2533, 0.1709) | I | 0.3242 | 13 |

13 | U_{42} | (85.6, 90.0, 2.5066, 0.4886) | II | 0.5959 | 7 |

**Table 7.**Calculation results of the cloud similarities between the overall cloud and SC for the SRA of the NPPBP in LXNPCL.

No. | Assessment Level | Similarity |
---|---|---|

1 | Outstanding | 0.3317 |

2 | Good | 0.1681 |

3 | Moderate | 2.0898 × 10^{−5} |

4 | General | 7.2700 × 10^{−25} |

5 | Unsatisfactory | 0.0141 |

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## Share and Cite

**MDPI and ACS Style**

Ding, R.; Liu, Z.
An IT2FS-ANP- and IT2FS-CM-Based Approach for Conducting Safety Risk Assessments of Nuclear Power Plant Building Projects. *Mathematics* **2024**, *12*, 1038.
https://doi.org/10.3390/math12071038

**AMA Style**

Ding R, Liu Z.
An IT2FS-ANP- and IT2FS-CM-Based Approach for Conducting Safety Risk Assessments of Nuclear Power Plant Building Projects. *Mathematics*. 2024; 12(7):1038.
https://doi.org/10.3390/math12071038

**Chicago/Turabian Style**

Ding, Rui, and Zehua Liu.
2024. "An IT2FS-ANP- and IT2FS-CM-Based Approach for Conducting Safety Risk Assessments of Nuclear Power Plant Building Projects" *Mathematics* 12, no. 7: 1038.
https://doi.org/10.3390/math12071038