本論文探討如何運用標記演算法來解模糊半指派問題。傳統指派問題屬於一對一指派，但在實務問題中，常會有分組、分群工作的情形，此時半指派問題的模型就能更貼切於這種實際狀況。此外，在許多現實情況中，我們無法完全掌握確切成本等參數或因為一些人為因素而有了不確定性，相較於傳統指派問題，成本不再是一個確定值而是一個範圍，我們可以利用模糊數更好的表達出這種不確定性的模型。
過去求解模糊運輸問題或模糊指派問題大多使用三角模糊數和梯形模糊數再利用順序函數(Ranking function)來將模糊集轉換成明確集(Crisp set)進行求解，本研究中，我們透過不同的方式來定義歸屬函數(Membership function)，包含管理者隨著總成本線性遞減的歸屬函數和個別員工指派成本在模糊區間線性遞增的歸屬函數。在同時看重管理者和員工的績效下進而建構出模糊半指派模型，再提出一演算法來解此模糊半指派問題，同時也以數值例的方式來呈現演算法的步驟流程。最後，透過參數的改變以及數據計算結果來分析結果是否符合預期並提供其管理意涵。

This thesis concentrates on using a labeling algorithm to solve fuzzy semi-assignment problem (semi-AP). The assignment problem is one-to-one assignment. However, in real-world applications, a task or project needs to be completed by a group of people. In this situation, semi-AP is more suitable than classic assignment problem. In addition, in real life situations, the costs of semi-AP may be imprecise. Also, human behavior in organization may cause uncertainty. In order to deal with these problems, we use the fuzzy number to express this uncertain situation.
In the past, most of fuzzy transportation problems and fuzzy assignment problems use triangular fuzzy number or trapezoidal fuzzy number then transform fuzzy set to crisp set by ranking function. In this study, we define the membership function through different viewpoint instead of using triangular fuzzy number or trapezoidal fuzzy number. The membership functions include manager’s perspective and workers’ perspective; the former is a decreasing linear membership function and the latter is increasing linear membership function. This study construct the fuzzy semi-AP based on emphasizing the performance of manager and workers equally and propose an algorithm to solve the fuzzy semi-AP. The numerical example is presented to demonstrate the procedure of the proposed algorithm. Finally, we change parameters to analyze the performances of the proposed algorithm and provide some management implications.

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