# Evaluation of Online Teaching Quality: An Extended Linguistic MAGDM Framework Based on Risk Preferences and Unknown Weight Information

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## Abstract

**:**

## 1. Introduction

- Inspired by the decision method in Lin and Wang [25], this framework extends the linguistic MAGDM method involving risk preferences from the single-level EIS to the multi-level one.
- In teaching quality evaluation problems based on multi-level EISs, many works of literature adopted the AHP approach to derive the weights of attributes and sub-attributes [8,9,10,11,12,13]. Sometimes AEs cannot make pairwise comparisons on the importance of attributes or sub-attributes, that is, they cannot use the AHP method to calculate attribute weights. Thus, based on the principle of maximizing the group comprehensive evaluation value of each alternative, a two-stage attribute and sub-attribute weight solution optimization model is established in this framework.
- The evaluation ranking results obtained by this framework are divided into the overall ranking result and partial ranking results, which are helpful for teachers and universities to understand their own situation and make targeted improvements.

## 2. Preliminaries

#### 2.1. Linguistic Term Set

**Definition**

**1.**

- The LTS$S$is ordered:${s}_{i}>{s}_{j}$if and only if$i>j$;
- There is a negation operator:$Neg({s}_{i})={s}_{-i}$where$Neg({s}_{0})={s}_{0}$.

#### 2.2. Group Generalized Linguistic Term Set

#### 2.2.1. Euclidean Distance

**Definition**

**2.**

#### 2.2.2. Score Function

#### 2.2.3. Group Generalized Linguistic Term Set Based on Risk Preferences

**Definition**

**3.**

#### 2.2.4. Determination of Risk Preference Parameters

## 3. EIS of Online Teaching Quality

#### 3.1. Selection of Indicators for Evaluating the Online Teaching Quality

#### 3.2. Determination of the Weights of Evaluation Indicators

## 4. A Method for Linguistic MAGDM Involving Risk Preferences and Completely Unknown Weight Information

## 5. A Case Study about Online Teaching Quality Evaluation

#### 5.1. Problem Description

#### 5.2. Evaluation of Online Teaching Quality among Four Teachers

## 6. Practical Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The brief flow of the two-stage sub-attribute and attribute weight solving optimization model.

Attribute | Sub-Attribute |
---|---|

Online teaching environment (${a}_{1}$) | Network environment (${a}_{11}$) |

Hardware equipment (${a}_{12}$) | |

Physical environment (${a}_{13}$) | |

Online teaching platform (${a}_{2}$) | Ease of operation (${a}_{21}$) |

Functionality (${a}_{22}$) | |

Personalized support (${a}_{23}$) | |

Online teaching content and methods (${a}_{3}$) | Teaching content (${a}_{31}$) |

Teaching schedule (${a}_{32}$) | |

Teaching format (${a}_{33}$) | |

Online classroom atmosphere (${a}_{4}$) | Influence of teaching (${a}_{41}$) |

Classroom atmosphere (${a}_{42}$) | |

Students’ attitudes to learning (${a}_{43}$) | |

Online teaching effectiveness (${a}_{5}$) | Level of knowledge acquired (${a}_{51}$) |

Level of thought-provoking (${a}_{52}$) | |

Problem-solving skills (${a}_{53}$) |

Attribute | Ranking |
---|---|

Online teaching environment $({a}_{1})$ | ${x}_{2}\stackrel{{a}_{1}}{\succ}{x}_{3}\stackrel{{a}_{1}}{\succ}{x}_{1}\stackrel{{a}_{1}}{\succ}{x}_{4}$ |

Online teaching platform $({a}_{2})$ | ${x}_{1}\stackrel{{a}_{2}}{\succ}{x}_{2}\stackrel{{a}_{2}}{\succ}{x}_{3}\stackrel{{a}_{2}}{\succ}{x}_{4}$ |

Online teaching content and methods $({a}_{3})$ | ${x}_{4}\stackrel{{a}_{3}}{\succ}{x}_{3}\stackrel{{a}_{3}}{\succ}{x}_{1}\stackrel{{a}_{3}}{\succ}{x}_{2}$ |

Online classroom atmosphere $({a}_{4})$ | ${x}_{2}\stackrel{{a}_{4}}{\succ}{x}_{3}\stackrel{{a}_{4}}{\succ}{x}_{1}\stackrel{{a}_{4}}{\succ}{x}_{4}$ |

Online teaching effectiveness $({a}_{5})$ | ${x}_{1}\stackrel{{a}_{5}}{\succ}{x}_{3}\stackrel{{a}_{5}}{\succ}{x}_{4}\stackrel{{a}_{5}}{\succ}{x}_{2}$ |

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**MDPI and ACS Style**

Lin, H.; You, J.; Xu, T.
Evaluation of Online Teaching Quality: An Extended Linguistic MAGDM Framework Based on Risk Preferences and Unknown Weight Information. *Symmetry* **2021**, *13*, 192.
https://doi.org/10.3390/sym13020192

**AMA Style**

Lin H, You J, Xu T.
Evaluation of Online Teaching Quality: An Extended Linguistic MAGDM Framework Based on Risk Preferences and Unknown Weight Information. *Symmetry*. 2021; 13(2):192.
https://doi.org/10.3390/sym13020192

**Chicago/Turabian Style**

Lin, Hui, Jianxin You, and Tao Xu.
2021. "Evaluation of Online Teaching Quality: An Extended Linguistic MAGDM Framework Based on Risk Preferences and Unknown Weight Information" *Symmetry* 13, no. 2: 192.
https://doi.org/10.3390/sym13020192