# Poverty Measure Based on Hesitant Fuzzy Decision Algorithm under Social Network Media

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Proposed Method

#### 3.1. Analysis of the Problems of Current Public Media Communication in Online Social Media

#### 3.1.1. “Light Public Welfare”

#### 3.1.2. “Public Welfare Fatigue”

#### 3.2. Multidimensional Poverty Measure Method

_{j}represents the poverty aversion coefficient on dimension j, S

_{j}is the set of the poor on the j dimension.

#### 3.3. Poverty Fuzzy Measure Method

_{A}(x)}, and μ

_{A}(x): X → [0, 1].

_{A}(x) is the membership function of fuzzy set A, the value of μ

_{A}(x) is the degree to which the element x belongs to the fuzzy set A. μ

_{A}(x) = 0 means that x does not belong to fuzzy set A, 0 < μA(x) < 1 means that the x part belongs to the fuzzy set A, and μA(x) = 1 means that x belongs completely to the fuzzy set A. Even with the same fuzzy meaning, the membership function may vary from case to case. A binary variable means that there are only two values 0 and 1, that is, the relationship between “Yes” and “No.” The dichotomous variable is the attribute indicating whether a family owns an asset. If it does, it means that the family is not poor in this dimension. Otherwise, it is poverty. The membership function of the binary variable is expressed as follows.

_{ij}indicates the degree of poverty of the ith family in the j dimension. X

_{ij}= 0 indicates that the variable is not poor in this dimension, and the value x

_{ij}= 1 indicates that it is inadequate.

_{min,j}and x

_{max},

_{j}respectively represent the maximum and minimum values of households on the jth dimension. If the variable takes the value x

_{ij}≤ x

_{min,j}, and the membership function value is 1, it is considered that the jth dimension of the family is poor. If the variable takes the value x

_{ij}≥ x

_{max,j}and the membership function value is 0, it is considered that the jth dimension of the family is not poor. If the value of the variable is between [x

_{min,j}, x

_{max},

_{j}], it means the poverty level of the family is between 0 and 1.

#### 3.4. Method for Calculating the Weight of Poverty Dimension

## 4. Experiments

## 5. Discussion

_{i}is as follows.

_{i}equal to the poverty rate index H = 12.00 based on the poverty line, and a = 8.2 after calculation.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Dimension | Variable | Poverty Standard |
---|---|---|

Economic situation | Income | Below the poverty line |

Educational level | Number of years of education | The average number of years of education for the family population is no more than five years. |

Environment | Drinking water | Do not drink tap water or groundwater over 5 m |

Sanitation facilities | No flush toilet | |

Living environment | There is excrement around the house | |

Lighting | Electricity can’t be used. | |

Fuel | Can’t use gas, natural gas, electricity | |

Health | Medical insurance | More than half of the household population does not have health insurance. |

Level of health | The average number of illnesses per family in the past month exceeded 0.5 times. | |

Asset status | House | Do not own the property right of the house |

Durable consumer goods | No more than two durable consumer goods |

Index | Income | Education | Drinking Water | Sanitation Facilities | Living Environment | Lighting |
---|---|---|---|---|---|---|

Incidence of poverty (%) | 17.4% | 45.8 | 16.8 | 45.9 | 39.8 | 32.6 |

Index | Fuel | Medical insurance | Level of health | House | Durable consumer goods | |

Incidence of poverty (%) | 41.6 | 4.5 | 14.2 | 23.8 | 38.5 |

**Table 3.**The change of poverty index after removing the dimensions of health facilities and education.

Poverty Dimensions K | Incidence of Poverty P(K) | Multidimensional Poverty Index M(K) | ||||
---|---|---|---|---|---|---|

Comparison Sample | Remove the Dimension of Sanitation Facilities | Remove the Dimension of Education | Comparison Sample | Remove the Dimension of Sanitation Facilities | Remove the Dimension of Education | |

1 | 89.6 | 86.4 | 86.1 | 27.7 | 24.8 | 25.9 |

2 | 70.9 | 63.1 | 61.5 | 26.2 | 20.7 | 22.8 |

3 | 45.6 | 28.4 | 33.8 | 19.0 | 14.2 | 17.0 |

4 | 27.3 | 13.7 | 15.2 | 14.2 | 0.1 | 9.1 |

5 | 12.9 | 5.1 | 7.2 | 8.1 | 4.0 | 4.4 |

6 | 4.4 | 2.1 | 2.8 | 3.5 | 1.4 | 1.9 |

7 | 2.1 | 0.4 | 0.4 | 1.8 | 0.3 | 0.3 |

8 | 0.4 | 0.3 | ||||

9 | 0.0 | 0.0 |

Dimension | Index | TRF | Weight | TFR Weighting | Contribution Rate % | ||
---|---|---|---|---|---|---|---|

Poverty Indicators System | Income | Income | 0.55 | 0.0418 | 0.0209 | 10.837 | 10.67 |

Education | Education | 0.561 | 0.0407 | 0.0209 | 10.727 | 10.57 | |

Environment | Drinking water | 0.3454 | 0.0693 | 0.022 | 11.42 | 42.17 | |

Sanitation facilities | 0.341 | 0.0704 | 0.022 | 11.398 | |||

Living environment | 0.1683 | 0.1122 | 0.0176 | 8.813 | |||

Lighting | 0.0077 | 0.297 | 0.0022 | 0.277 | |||

Fuel | 0.2189 | 0.0968 | 0.0187 | 9.979 | |||

Health | Medical insurance | 0.2816 | 0.0814 | 0.0209 | 10.814 | 20.31 | |

Level of health | 0.2013 | 0.1012 | 0.0187 | 9.627 | |||

Asset status | House | 0.0836 | 0.154 | 0.0121 | 5.755 | 16.28 | |

Durable consumer goods | 0.5951 | 0.0363 | 0.0198 | 10.353 | |||

Total | 100 | 100 |

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**MDPI and ACS Style**

Gao, S.; Sun, K.
Poverty Measure Based on Hesitant Fuzzy Decision Algorithm under Social Network Media. *Symmetry* **2020**, *12*, 384.
https://doi.org/10.3390/sym12030384

**AMA Style**

Gao S, Sun K.
Poverty Measure Based on Hesitant Fuzzy Decision Algorithm under Social Network Media. *Symmetry*. 2020; 12(3):384.
https://doi.org/10.3390/sym12030384

**Chicago/Turabian Style**

Gao, Suwei, and Kaiyang Sun.
2020. "Poverty Measure Based on Hesitant Fuzzy Decision Algorithm under Social Network Media" *Symmetry* 12, no. 3: 384.
https://doi.org/10.3390/sym12030384