# A Multi-Criteria Group Decision-Making Method for Risk Assessment of Live-Streaming E-Commerce Platform

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*J. Theor. Appl. Electron. Commer. Res.*

**2023**,

*18*(2), 1126-1141; https://doi.org/10.3390/jtaer18020057

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. The Risks of the Live-Streaming E-Commerce Platforms

#### 2.2. Risk Assessment Methods for Live-Streaming E-Commerce Platforms

## 3. Overview of Interval-Valued Intuitionistic Fuzzy Sets

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

- (a)
- $\tilde{\alpha}+\tilde{\beta}=\left(\left[{a}_{1}+{a}_{2}-{a}_{1}{a}_{2},{b}_{1}+{b}_{2}-{b}_{1}{b}_{2}\right],\left[{c}_{1}{c}_{2},{d}_{1}{d}_{2}\right]\right)$;
- (b)
- $\tilde{\alpha}\cdot \tilde{\beta}=\left(\left[{a}_{1}{a}_{2},{b}_{1}{b}_{2}\right],\left[{c}_{1}+{c}_{2}-{c}_{1}{c}_{2},{d}_{1}+{d}_{2}-{d}_{1}{d}_{2}\right]\right)$;
- (c)
- $\lambda \tilde{\alpha}=\left(\left[1-{\left(1-{a}_{1}\right)}^{\lambda},1-{\left(1-{b}_{1}\right)}^{\lambda}\right],\left[{c}_{1}{}^{\lambda},{d}_{1}{}^{\lambda}\right]\right)$;
- (d)
- ${\tilde{\alpha}}^{\lambda}=\left(\left[{a}_{1}^{\lambda},{b}_{1}^{\lambda}\right],\left[1-{\left(1-{c}_{1}\right)}^{\lambda},1-{\left(1-{d}_{1}\right)}^{\lambda}\right]\right)$.

**Definition**

**4.**

**Definition**

**5.**

## 4. Risk Assessment Model of Live-Streaming E-Commerce Platform

#### 4.1. Problem Description

- (a)
- $A=\left\{{A}_{1},{A}_{2},\dots ,{A}_{m}\right\}$: The set of m alternative live-streaming e-commerce platforms concerned by decision-makers, where ${A}_{i}$ represents the i-th alternative live-streaming e-commerce platform, $i=1,2,\dots ,m$.
- (b)
- $U=\left\{{u}_{1},{u}_{2},\dots ,{u}_{n}\right\}$: The set of n risk criteria that decision-makers pay attention to when evaluating the risk of the live-streaming e-commerce platform, where ${u}_{j}$ represents the j-th risk criterion, $j=1,2,\dots ,n$.
- (c)
- $E=\left\{{e}_{1},{e}_{2},\dots ,{e}_{n}\right\}$: s decision-makers participating in the decision, where ${e}_{k}$ represents the k-th decision-maker, $k=1,2,\dots ,s$.
- (d)
- $\omega =\left\{{\omega}_{1},{\omega}_{2},\dots ,{\omega}_{j}\right\}$: Weight vector of risk criteria, where ${\omega}_{j}$ represents the weight or importance of the risk criterion, satisfying ${\omega}_{j}\ge 0$ and $\sum _{j=1}^{n}{\omega}_{j}=1,j=1,2,\dots ,n$. Here, the weight vector of the risk criterion can be given by the decision-maker.
- (e)
- ${\lambda}_{j}^{k}$: Weight of decision-maker ${e}_{k}$ for risk criterion ${u}_{j}$.
- (f)
- ${r}_{ij}^{k}=\left(\left[{a}_{ij}^{k},{b}_{ij}^{k}\right],\left[{c}_{ij}^{k},{d}_{ij}^{k}\right]\right)$: The evaluation value of the decision-maker ${e}_{k}$ on the risk criterion ${u}_{j}$ of the alternative live-streaming e-commerce platform ${A}_{i}$, which is an interval-valued intuition fuzzy number, where $\left[{a}_{ij}^{k},{b}_{ij}^{k}\right]$ and $\left[{c}_{ij}^{k},{d}_{ij}^{k}\right]$ represent the decision-maker’s membership degree and non-membership degree of the alternative live-streaming e-commerce platform ${A}_{i}$ on the risk criterion ${u}_{j}$, respectively. Further, $\left[{a}_{ij}^{k},{b}_{ij}^{k}\right]\subseteq \left[0,1\right],\left[{c}_{ij}^{k},{d}_{ij}^{k}\right]\subseteq \left[0,1\right],{b}_{ij}^{k}+{d}_{ij}^{k}\le 1$.
- (g)
- $\tilde{{R}^{k}}={\left(\tilde{{r}_{ij}^{k}}\right)}_{m\times n}$: The risk assessment matrix of decision-maker ${e}_{k}$.
- (h)
- $T=\left\{{T}^{1},{T}^{2},\dots ,{T}^{v}\right\}$: The set of evaluation scales about the decision-makers’ professionalism for risk criteria. Where ${T}^{\epsilon}$ represents the $\mathit{\epsilon}$-th evaluation scale, $\epsilon =1,2,\dots ,v$. Generally, the larger $\epsilon $, the corresponding evaluation level is higher. For instance, in the specific example in the fifth part of this article, regarding the decision-maker’ scoring of the professionalism for the risk criteria, the scale set used is in the form of a 5-point scale, namely $T=\left\{{T}^{1}=1,{T}^{2}=2,{T}^{3}=3,{T}^{4}=4,{T}^{5}=5\right\}$. Where 1 indicates the least professionalism, and 5 indicates the highest professionalism.
- (i)
- ${q}_{gj}^{k}={T}^{\epsilon}$: The professional score value of decision-maker ${e}_{g}$ on the risk criterion ${u}_{j}$ for decision-maker ${e}_{\mathrm{k}}$, where ${e}_{g}$ represents the g-th decision-maker, $g=1,2,\dots ,n$.

#### 4.2. Risk Assessment Model of Live-Streaming E-Commerce Platform

## 5. Case Study

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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${\mathit{u}}_{1}$ | ${\mathit{u}}_{2}$ | ${\mathit{u}}_{3}$ | ${\mathit{u}}_{4}$ | ${\mathit{u}}_{5}$ | ||
---|---|---|---|---|---|---|

${e}_{1}$ | ${A}_{1}$ | ([0.6,0.8], [0.1,0.2]) | ([0.6,0.75], [0.05,0.2]) | ([0.6,0.65], [0.05,0.3]) | ([0.3,0.45], [0.35,0.4]) | ([0.4,0.5], [0.35,0.4]) |

${A}_{2}$ | ([0.7,0.8], [0.05,0.1]) | ([0.5,0.65], [0.25,0.3]) | ([0.45,0.6], [0.05,0.3]) | ([0.35,0.5], [0.3,0.4]) | ([0.45,0.5], [0.3,0.45]) | |

${A}_{3}$ | ([0.4,0.6], [0.15,0.3]) | ([0.45,0.6], [0.2,0.35]) | ([0.7,0.85], [0.05,0.1]) | ([0.35,0.6], [0.25,0.3]) | ([0.4,0.45], [0.5,0.65]) | |

${A}_{4}$ | ([0.3,0.5], [0.35,0.4]) | ([0.35,0.5], [0.35,0.45]) | ([0.6,0.75], [0.05,0.2]) | ([0.65,0.7], [0.15,0.5]) | ([0.25,0.3], [0.4,0.6]) | |

${A}_{5}$ | ([0.3,0.45, [0.35,0.5]) | ([0.65,0.8], [0.05,0.15]) | ([0.3,0.45], [0.45,0.5]) | ([0.55,0.6], [0.3,0.35]) | ([0.3,0.4], [0.3,0.55]) | |

${e}_{2}$ | ${A}_{1}$ | ([0.5,0.8], [0.05,0.2]) | ([0.65,0.75], [0.05,0.2]) | ([0.5,0.65], [0.05,0.3]) | ([0.3,0.55], [0.25,0.3]) | ([0.3,0.45], [0.45,0.5]) |

${A}_{2}$ | ([0.5,0.7], [0.15,0.3]) | ([0.65,0.7], [0.15,0.3]) | ([0.5,0.65], [0.15,0.3]) | ([0.25,0.4], [0.3,0.45]) | ([0.55,0.6], [0.3,0.4]) | |

${A}_{3}$ | ([0.45,0.7], [0.05,0.2]) | ([0.4,0.55], [0.2,0.45]) | ([0.65,0.7], [0.15,0.25]) | ([0.4,0.55], [0.25,0.4]) | ([0.35,0.5], [0.4,0.45]) | |

${A}_{4}$ | ([0.35,0.6], [0.15,0.3]) | ([0.55,0.7], [0.15,0.25]) | ([0.55,0.7], [0.15,0.2]) | ([0.55,0.8], [0.05,0.1]) | ([0.25,0.3], [0.4,0.7]) | |

${A}_{5}$ | ([0.35,0.6], [0.35,0.4]) | ([0.65,0.7], [0.15,0.2]) | ([0.45,0.5], [0.2,0.35]) | ([0.45,0.8], [0.1,0.15]) | ([0.25,0.3], [0.45,0.7]) | |

${e}_{3}$ | ${A}_{1}$ | ([0.45,0.7], [0.15,0.2]) | ([0.55,0.6], [0.15,0.25]) | ([0.45,0.6], [0.25,0.3]) | ([0.45,0.5], [0.25,0.3]) | ([0.35,0.4], [0.45,0.5]) |

${A}_{2}$ | ([0.55,0.6], [0.15,0.2]) | ([0.55,0.7], [0.15,0.25]) | ([0.55,0.6], [0.15,0.4]) | ([0.35,0.5], [0.3,0.4]) | ([0.4,0.6], [0.35,0.4]) | |

${A}_{3}$ | ([0.4,0.65], [0.15,0.3]) | ([0.35,0.45], [0.4,0.55]) | ([0.6,0.75], [0.2,0.25]) | ([0.45,0.5], [0.2,0.45]) | ([0.35,0.5], [0.4,0.45]) | |

${A}_{4}$ | ([0.55,0.6], [0.15,0.3]) | ([0.55,0.65], [0.05,0.2]) | ([0.55,0.7], [0.15,0.3]) | ([0.55,0.7], [0.05,0.2]) | ([0.15,0.2], [0.4,0.75]) | |

${A}_{5}$ | ([0.45,0.5], [0.3,0.45]) | ([0.5,0.7], [0.15,0.25]) | ([0.35,0.4], [0.25,0.4]) | ([0.65,0.8], [0.05,0.1]) | ([0.05,0.2], [0.55,0.7]) | |

${e}_{4}$ | ${A}_{1}$ | ([0.55,0.7], [0.2,0.25]) | ([0.45,0.7], [0.15,0.3]) | ([0.55,0.6], [0.3,0.35]) | ([0.55,0.6], [0.2,0.35]) | ([0.35,0.4], [0.4,0.55]) |

${A}_{2}$ | ([0.45,0.6], [0.15,0.3]) | ([0.5,0.7], [0.15,0.25]) | ([0.45,0.6], [0.25,0.4]) | ([0.3,0.55], [0.3,0.45]) | ([0.3,0.6], [0.35,0.4]) | |

${A}_{3}$ | ([0.45,0.6], [0.15,0.3]) | ([0.35,0.4], [0.4,0.6]) | ([0.6,0.7], [0.2,0.3]) | ([0.4,0.55], [0.35,0.4]) | ([0.35,0.6], [0.25,0.3]) | |

${A}_{4}$ | ([0.55,0.7], [0.15,0.4]) | ([0.5,0.65], [0.05,0.35]) | ([0.55,0.7], [0.15,0.2]) | ([0.55,0.7], [0.15,0.2]) | ([0.2,0.4], [0.5,0.6]) | |

${A}_{5}$ | ([0.4,0.55], [0.35,0.4]) | ([0.5,0.75], [0.15,0.25]) | ([0.35,0.5], [0.45,0.5]) | ([0.65,0.8], [0.05,0.2]) | ([0.05,0.3], [0.55,0.7]) |

${\mathit{u}}_{1}$ | ${\mathit{u}}_{2}$ | ${\mathit{u}}_{3}$ | ${\mathit{u}}_{4}$ | ${\mathit{u}}_{5}$ | ||
---|---|---|---|---|---|---|

${e}_{1}$ | ${e}_{1}$ | 2 | 1 | 3 | 2 | 4 |

${e}_{2}$ | 2 | 3 | 4 | 2 | 5 | |

${e}_{3}$ | 3 | 4 | 1 | 4 | 3 | |

${e}_{4}$ | 4 | 5 | 2 | 3 | 2 | |

${e}_{2}$ | ${e}_{1}$ | 1 | 3 | 4 | 2 | 4 |

${e}_{2}$ | 3 | 2 | 3 | 1 | 5 | |

${e}_{3}$ | 4 | 4 | 3 | 3 | 3 | |

${e}_{4}$ | 4 | 3 | 2 | 5 | 2 | |

${e}_{3}$ | ${e}_{1}$ | 2 | 1 | 4 | 1 | 5 |

${e}_{2}$ | 2 | 3 | 5 | 2 | 3 | |

${e}_{3}$ | 4 | 3 | 2 | 5 | 3 | |

${e}_{4}$ | 4 | 3 | 2 | 3 | 1 | |

${e}_{4}$ | ${e}_{1}$ | 1 | 3 | 3 | 2 | 4 |

${e}_{2}$ | 2 | 1 | 5 | 1 | 3 | |

${e}_{3}$ | 4 | 4 | 1 | 3 | 3 | |

${e}_{4}$ | 4 | 5 | 1 | 4 | 2 |

${\mathit{u}}_{2}$ | ${\mathit{u}}_{2}$ | ${\mathit{u}}_{3}$ | ${\mathit{u}}_{4}$ | ${\mathit{u}}_{5}$ | |
---|---|---|---|---|---|

${e}_{1}$ | 3 | 4 | 7 | 3.5 | 8.5 |

${e}_{2}$ | 4.5 | 4.5 | 8.5 | 3 | 8 |

${e}_{3}$ | 7.5 | 7.5 | 3.5 | 7.5 | 6 |

${e}_{4}$ | 8 | 8 | 3.5 | 7.5 | 3.5 |

${\mathit{u}}_{1}$ | ${\mathit{u}}_{2}$ | ${\mathit{u}}_{3}$ | ${\mathit{u}}_{4}$ | ${\mathit{u}}_{5}$ | |
---|---|---|---|---|---|

${e}_{1}$ | 0.13 | 0.17 | 0.30 | 0.16 | 0.33 |

${e}_{2}$ | 0.20 | 0.19 | 0.38 | 0.14 | 0.31 |

${e}_{3}$ | 0.32 | 0.31 | 0.16 | 0.35 | 0.23 |

${e}_{4}$ | 0.35 | 0.33 | 0.16 | 0.35 | 0.13 |

${\mathit{u}}_{1}$ | ${\mathit{u}}_{2}$ | ${\mathit{u}}_{3}$ | ${\mathit{u}}_{4}$ | ${\mathit{u}}_{5}$ | |
---|---|---|---|---|---|

${A}_{1}$ | ([0.52,0.75],[0.10,0.22]) | ([0.55,0.70],[0.10,0.25]) | ([0.55,0.65],[0.15,0.34]) | ([0.45,0.57],[0.27,0.36]) | ([0.37,0.46],[0.43,0.51]) |

${A}_{2}$ | ([0.53,0.68],[0.10,0.19]) | ([0.55,0.69],[0.16,0.27]) | ([0.49,0.64],[0.15,0.40]) | ([0.32,0.54],[0.30,0.43]) | ([0.46,0.58],[0.33,0.41]) |

${A}_{3}$ | ([0.43,0.67],[0.11,0.30]) | ([0.38,0.48],[0.32,0.51]) | ([0.65,0.78],[0.15,0.24]) | ([0.43,0.55],[0.25,0.38]) | ([0.37,0.52],[0.35,0.44]) |

${A}_{4}$ | ([0.49,0.65],[0.20,0.36]) | ([0.50,0.64],[0.08,0.30]) | ([0.57,0.74],[0.12,0.25]) | ([0.57,0.75],[0.08,0.25]) | ([0.22,0.32],[0.43,0.66]) |

${A}_{5}$ | ([0.40,0.55],[0.34,0.45]) | ([0.56,0.74],[0.13,0.22]) | ([0.38,0.50],[0.34,0.45]) | ([0.61,0.81],[0.11,0.20]) | ([0.20,0.32],[0.48,0.69]) |

${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | ${\mathit{A}}_{4}$ | ${\mathit{A}}_{5}$ | |
---|---|---|---|---|---|

$d\left({A}_{i},\tilde{{X}^{+}}\right)$ | 0.38 | 0.37 | 0.38 | 0.39 | 0.47 |

$d\left({A}_{i},\tilde{{X}^{-}}\right)$ | 0.62 | 0.63 | 0.62 | 0.61 | 0.53 |

${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{A}}_{3}$ | ${\mathit{A}}_{4}$ | ${\mathit{A}}_{5}$ | |
---|---|---|---|---|---|

$r\left({A}_{i}\right)$ | 0.3825 | 0.3749 | 0.3753 | 0.3931 | 0.4715 |

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## Share and Cite

**MDPI and ACS Style**

Su, J.; Wang, D.; Zhang, F.; Xu, B.; Ouyang, Z.
A Multi-Criteria Group Decision-Making Method for Risk Assessment of Live-Streaming E-Commerce Platform. *J. Theor. Appl. Electron. Commer. Res.* **2023**, *18*, 1126-1141.
https://doi.org/10.3390/jtaer18020057

**AMA Style**

Su J, Wang D, Zhang F, Xu B, Ouyang Z.
A Multi-Criteria Group Decision-Making Method for Risk Assessment of Live-Streaming E-Commerce Platform. *Journal of Theoretical and Applied Electronic Commerce Research*. 2023; 18(2):1126-1141.
https://doi.org/10.3390/jtaer18020057

**Chicago/Turabian Style**

Su, Jiafu, Dan Wang, Fengting Zhang, Baojian Xu, and Zhiguang Ouyang.
2023. "A Multi-Criteria Group Decision-Making Method for Risk Assessment of Live-Streaming E-Commerce Platform" *Journal of Theoretical and Applied Electronic Commerce Research* 18, no. 2: 1126-1141.
https://doi.org/10.3390/jtaer18020057