# Light Pollution Index System Model Based on Markov Random Field

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## Abstract

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## 1. Introduction

- During the establishment of the Markov random field model, the weights obtained by the entropy weight method were multiplied by variables in the activation function, and the importance of different variables was reflected in the model so that the established model can more scientifically and accurately assess the severity of light pollution.
- The established optimization model provides a scientific theory basis for selecting the best intervention strategy for the determined location.
- After building the model, we conducted a comprehensive experiment on five data sets to check the validity of our model, and the test results show that the model is very effective.

## 2. Development of a Broadly Applicable Metric

#### 2.1. Index Determination and Data Collection

#### 2.2. The Establishment of LBLPRAI

- Protected land: Areas that are protected by government or private entities from development for their ecological, cultural, and natural importance;
- Rural community: A community located in one of the sparsely populated areas of a country or region and is not easily accessible from urban communities;
- Suburban communities: Located in areas with moderate population density in a country or region or easily accessible from urban communities;
- Urban community: A community located in one of a country or region’s most densely populated areas.

#### 2.3. LBLPRAI of Four Diverse Types of Locations

## 3. Three Possible Intervention Strategies to Address Light Pollution

#### 3.1. Three Possible Intervention Strategies

- (1)
- Roadway lighting systems planning

- (2)
- Increasing vegetation coverage

- (3)
- Building system planning

#### 3.2. Potential Impacts

#### 3.3. Analysis and Evaluation

## 4. Effect of Intervention Strategies on LBLPRAI at Two Locations

#### 4.1. Establishment of Influence Model

#### 4.2. Influence Model Solving

#### 4.3. Influence Model Improvement

## 5. Conclusions and Future Work

- When selecting indicators to assess the severity of light pollution in a specific location, 12 indicators were carefully selected. The combination of an R-type clustering algorithm and correlation analysis was used to screen the indicators, and the ten indicators finally selected can more accurately reflect the characteristics of different regions, covering all aspects of our living environment, more comprehensively assess the light pollution level in different regions, and better understand the relationship between light pollution degree and various factors causing light pollution in different regions.
- Different sites were divided into four types for light pollution assessment. The cumulative distribution probability was used to analyze the degree of light pollution of different types of sites and interpret the results, which can intuitively see the impact and relationship of four different types of regions on the risk level of light pollution under the selected indicators.
- The authors considered that different strategies will not only lead to changes in the risk level of light pollution but also affect potential indicators. Partial least squares regression was used to study the multicollinearity relationship between the indicator variables and the three potential impact indicators, determining that it has a strong ability to explain the dependent variables. After putting forward three possible intervention strategies for light pollution, the potential impact of each strategy on the overall impact of light pollution was evaluated using a partial least squares regression model.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

${x}_{1}$ | Disposable income per capita and number of cars per capita |

${x}_{2}$ | Floor area of the building |

${x}_{3}$ | Proportion of urban population |

${x}_{4}$ | Electricity consumption per capita |

${x}_{5}$ | Night light intensity |

${x}_{6}$ | Density of population |

${x}_{7}$ | Amount of precipitation |

${x}_{8}$ | Medial humidity and average temperature |

${x}_{9}$ | Vegetation coverage |

${x}_{10}$ | Number of species |

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**Figure 10.**(

**a**) Intervention strategy (1) impact on light pollution level and crime rate; (

**b**) intervention strategy (1) impact on accident rate and sleep time.

**Figure 11.**(

**a**) Intervention strategy (2) impact on light pollution level and crime rate; (

**b**) intervention strategy (2) impact on accident rate and sleep time.

**Figure 12.**(

**a**) Intervention strategy (3) impact on light pollution level and crime rate; (

**b**) intervention strategy (3) impact on accident rate and sleep time.

Region | LBLPRAI | Rank |
---|---|---|

Protected Land | 0.02757 | 5 |

Rural Community | 0.10872 | 4 |

Suburban Community | 0.15159 | 3 |

Urban Community 1 | 0.29164 | 2 |

Urban Community 2 | 0.42049 | 1 |

Validity Index | $\mathbf{\u2206}\mathit{P}$ | $\mathbf{\u2206}{\mathit{z}}_{1}$ | $\mathbf{\u2206}{\mathit{z}}_{2}$ | $\mathbf{\u2206}{\mathit{z}}_{3}$ |
---|---|---|---|---|

$\u2206P$ | 1 | 2 | 2 | 3 |

$\u2206{z}_{1}$ | 1/2 | 1 | 1 | 2 |

$\u2206{z}_{2}$ | 1/2 | 1 | 1 | 2 |

$\u2206{z}_{3}$ | 1/3 | 1/2 | 1/2 | 1 |

Rural Community | $\mathit{\mu}$ | $\mathit{H}$ | Urban Community 2 | $\mathit{\mu}$ | $\mathit{H}$ |
---|---|---|---|---|---|

Intervention Strategy (1) | 0.53 | 0.02 | Intervention Strategy (1) | 0.82 | 0.25 |

Intervention Strategy (2) | 0.66 | 0.03 | Intervention Strategy (2) | 0.54 | 0.04 |

Intervention Strategy (3) | 0.89 | 0.01 | Intervention Strategy (3) | 0.74 | 0.11 |

Rural Community | $\mathit{\mu}$ | $\mathit{H}$ | Urban Community 2 | $\mathit{\mu}$ | $\mathit{H}$ |
---|---|---|---|---|---|

Intervention Strategy (1) | 0.56 | 0.044 | Intervention Strategy (1) | 0.84 | 0.261 |

Intervention Strategy (2) | 0.92 | Intervention Strategy (2) | 0.71 | ||

Intervention Strategy (3) | 0.69 | Intervention Strategy (3) | 0.52 |

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**MDPI and ACS Style**

Fang, L.; Wu, Z.; Tao, Y.; Gao, J.
Light Pollution Index System Model Based on Markov Random Field. *Mathematics* **2023**, *11*, 3030.
https://doi.org/10.3390/math11133030

**AMA Style**

Fang L, Wu Z, Tao Y, Gao J.
Light Pollution Index System Model Based on Markov Random Field. *Mathematics*. 2023; 11(13):3030.
https://doi.org/10.3390/math11133030

**Chicago/Turabian Style**

Fang, Liangkun, Zhangjie Wu, Yuan Tao, and Jinfeng Gao.
2023. "Light Pollution Index System Model Based on Markov Random Field" *Mathematics* 11, no. 13: 3030.
https://doi.org/10.3390/math11133030