針對選擇圖書館方案決策影響因素的資訊不完全性以及影響因素間與評價指標的灰色關聯性，綜合應用灰色系統理論、向量投影原理和模糊數學理論，在灰色關聯投影法的基礎上，提出了一種選擇圖書館方案優選的TOPSIS-灰關聯投影法。實例分析表明，採用該方法具有科學實用、操作簡便、易於實現程式化、決策靈敏度高等特性，能夠為方案的決策提供更為可靠的依據，具有一定的推廣和實用價值。本文提出了利用TOPSIS法從選擇圖書館方案的理想解和負理想解在多維空間上的實際距離度量其優劣以及灰色關聯投影法從選擇圖書館方案指標序列與最優序列和最劣序列在幾何形狀上的關聯度來度量其優劣順序。最後將採用熵權法與TOPSIS、灰色關聯投影法結合起來，更全面對產品的品質進行優劣排序，並進行實例分析，排序結果符合客觀實際。

According to the characteristics of the decision factors of the library selection, such as information incompleteness and their grey correlation, using grey system theory, vector projection synthetically and fuzzy mathematic theory, a TOPSIS-grey relation projection method for the optimization of the Library selection is established based on the grey relation projection method. The paper use the TOPSIS method to measure the superior or inferior minor of the actual distance from the library selection solution to the ideal solution and negative ideal solution in a multidimensional space. The paper was through the associated of geometry measure the superior and inferior from the sequence to the optimal and the worst sequence based on grey relation projection method. Finally, combining entropy weight with TOPSIS and grey relation projection of the two methods can be more comprehensive to sort the superior and inferior of the library selection, and sort of instance analysis results fulfill with the objective reality.