# Fuzzy Decision-Making and Resource Management Model of Performance Evaluation Indices

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## Abstract

**:**

## 1. Introduction

## 2. Fuzzy Evaluation Rules for Satisfaction Index

- (1)
- If ${Z}_{Sh0}<{d}_{Sh0}$, then ${d}_{hR}/{d}_{T}<\varphi $. Therefore, we reject ${H}_{0}$ and draw the conclusion ${I}_{Sh}<{I}_{S0}$. Thus, Service Item h needs to be improved.
- (2)
- If ${Z}_{Sh0}\ge {d}_{Sh0}$, then ${d}_{hR}/{d}_{T}\ge \varphi $. Thus, we do not reject ${H}_{0}$ and draw the conclusion ${I}_{Sh}\ge {I}_{S0}$. Thus, Service Item h does not need to be improved.

## 3. Fuzzy Evaluation Rules for Importance Index

- (1)
- If ${Z}_{Ih0}>{d}_{Ih0}$, then ${d}_{hR}^{\prime}/{d}_{T}^{\prime}<\varphi $. Therefore, we reject ${H}_{0}$ and draw the conclusion ${I}_{Ih}>{I}_{I0}$. Consequently, Service Item h has a high priority for improvement.
- (2)
- If ${Z}_{Ih0}\le {d}_{Ih0}$, then ${d}_{hR}^{\prime}/{d}_{T}^{\prime}\ge \varphi $. Therefore, we do not reject ${H}_{0}$ and draw the conclusion ${I}_{Ih}\le {I}_{I0}$. Consequently, Service Item h has a low priority for improvement.

## 4. An Application Example

- The course material that the teacher has prepared is at an adequate level of complexity (X
_{1}, Y_{1}). - The quantity of the material is appropriate (X
_{2}, Y_{2}). - The content of the material helps improve my foreign language proficiency (X
_{3}, Y_{3}). - The teacher has prepared thoroughly for the class (X
_{4}, Y_{4}).

- 5.
- The teacher emphasizes conversation practice in a foreign language (X
_{5}, Y_{5}). - 6.
- The teacher values the opinions of students (X
_{6}, Y_{6}). - 7.
- Student-teacher interaction in class is intensive (X
_{7}, Y_{7}). - 8.
- The teacher is happy to help students solve problems (X
_{8}, Y_{8}). - 9.
- The teacher treats all students fairly (X
_{9}, Y_{9}).

- 10.
- The teacher speaks the foreign language clearly (X
_{10}, Y_{10}). - 11.
- The teacher expresses himself/herself logically (X
_{11}, Y_{11}).

- 12.
- The teacher uses a variety of teaching methods (X
_{12}, Y_{12}). - 13.
- The teacher interests me in learning the foreign language (X
_{13}, Y_{13}). - 14.
- The teacher adequately controls the pace of teaching (X
_{14}, Y_{14}).

- 15.
- The coursework or evaluation helps me improve my foreign language proficiency (X
_{15}, Y_{15}). - 16.
- Evaluation is at an adequate level of complexity (X
_{16}, Y_{16}).

## 5. Conclusions, Research Limitations and Future Research

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Membership function ${\eta}^{\prime}\left(x\right)$ with the vertical line of $x$ $=$ ${Z}_{Ih0}$.

Dimensions/Item | ${\widehat{\mathit{I}}}_{\mathit{S}\mathit{h}\mathbf{0}}$ | ${\mathit{Z}}_{\mathit{S}\mathit{h}\mathbf{0}}$ | Remark |
---|---|---|---|

Dimension 1: Teaching Preparation | |||

- The course material that the teacher has prepared is at an adequate level of complexity.
| 0.72 | 1.95 | |

- 2.
- The quantity of the material is appropriate.
| 0.69 | 0.89 | |

- 3.
- The content of the material helps improve my foreign language proficiency.
| 0.76 | 2.24 | |

- 4.
- The teacher has prepared thoroughly for the class.
| 0.52 | −2.79 | Improve |

Dimension 2: Teaching Attitude | |||

- 5.
- The teacher emphasizes conversation practice in a foreign language.
| 0.67 | 0.45 | |

- 6.
- The teacher values the opinions of students.
| 0.49 | −2.76 | Improve |

- 7.
- Student-teacher interaction in class is intensive.
| 0.68 | 0.54 | |

- 8.
- The teacher is happy to help students solve problems.
| 0.51 | −3.27 | Improve |

- 9.
- The teacher treats all students fairly.
| 0.69 | 0.82 | |

Dimension 3: Teaching Capability | |||

- 10.
- The teacher speaks the foreign language clearly.
| 0.71 | 1.22 | |

- 11.
- The teacher expresses himself/herself logically.
| 0.73 | 1.61 | |

Dimension 4: Teaching Management | |||

- 12.
- The teacher uses a variety of teaching methods.
| 0.69 | 0.73 | |

- 13.
- The teacher interests me in learning a foreign language.
| 0.65 | −0.11 | Improve |

- 14.
- The teacher adequately controls the pace of teaching.
| 0.54 | −2.37 | Improve |

Dimension 5: Coursework and Evaluation | |||

- 15.
- The coursework or evaluation helps me improve my foreign language proficiency.
| 0.72 | 1.40 | |

- 16.
- Evaluation is at an adequate level of complexity.
| 0.69 | 0.92 |

Dimensions/Item | ${\widehat{\mathit{I}}}_{\mathit{I}\mathit{h}0}$ | ${\mathit{Z}}_{\mathit{I}\mathit{h}0}$ | Priority |
---|---|---|---|

Dimension 1: Teaching Preparation | |||

- The course material that the teacher has prepared is at an adequate level of complexity.
| 0.75 | 1.68 | |

- 2.
- The quantity of the material is appropriate.
| 0.68 | −0.05 | |

- 3.
- The content of the material helps improve my foreign language proficiency.
| 0.73 | 2.03 | |

- 4.
- The teacher has prepared thoroughly for the class.
| 0.59 | −2.15 | Low |

Dimension 2: Teaching Attitude | |||

- 5.
- The teacher emphasizes conversation practice in a foreign language.
| 0.58 | −3.00 | |

- 6.
- The teacher values the opinions of students.
| 0.78 | 1.23 | High |

- 7.
- Student-teacher interaction in class is intensive.
| 0.72 | 0.84 | |

- 8.
- The teacher is happy to help students solve problems.
| 0.56 | −2.86 | Low |

- 9.
- The teacher treats all students fairly.
| 0.57 | −2.84 | |

Dimension 3: Teaching Capability | |||

- 10.
- The teacher speaks the foreign language clearly.
| 0.82 | 2.80 | |

- 11.
- The teacher expresses himself/herself logically.
| 0.71 | 0.56 | |

Dimension 4: Teaching Management | |||

- 12.
- The teacher uses a variety of teaching methods.
| 0.66 | −0.52 | |

- 13.
- The teacher interests me in learning a foreign language.
| 0.61 | −1.83 | Low |

- 14.
- The teacher adequately controls the pace of teaching.
| 0.80 | 2.73 | High |

Dimension 5: Coursework and Evaluation | |||

- 15.
- The coursework or evaluation helps me improve my foreign language proficiency.
| 0.74 | 1.32 | |

- 16.
- Evaluation is at an adequate level of complexity.
| 0.61 | −1.86 |

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**MDPI and ACS Style**

Chen, K.-S.; Hsieh, T.-H.; Chang, C.-P.; Yao, K.-C.; Huang, T.-H.
Fuzzy Decision-Making and Resource Management Model of Performance Evaluation Indices. *Axioms* **2024**, *13*, 198.
https://doi.org/10.3390/axioms13030198

**AMA Style**

Chen K-S, Hsieh T-H, Chang C-P, Yao K-C, Huang T-H.
Fuzzy Decision-Making and Resource Management Model of Performance Evaluation Indices. *Axioms*. 2024; 13(3):198.
https://doi.org/10.3390/axioms13030198

**Chicago/Turabian Style**

Chen, Kuen-Suan, Tsung-Hua Hsieh, Chia-Pao Chang, Kai-Chao Yao, and Tsun-Hung Huang.
2024. "Fuzzy Decision-Making and Resource Management Model of Performance Evaluation Indices" *Axioms* 13, no. 3: 198.
https://doi.org/10.3390/axioms13030198