中文摘要：

针对属性权重完全未知且属性值为三角模糊数的多属性决策问题，本文提出了一种基于线性规划和模糊向量投影的决策方法。该方法给出了三角模糊数向量投影、相对贴近度等概念，基于加权属性值离差最大化建立一个线性规划模型，通过求解此模型得到属性的权重，从而计算各方案的加权属性值在模糊正理想点和负理想解上的投影，进而计算相对贴近度，并据此对方案进行排序。最后，通过算例说明模型及方法的可行性和有效性。

英文摘要：

With regard to the fuzzy multi-attribute decision making （FMADM） problems, in which the information about attribute weights are unknown completely and the attribute values are in the form of triangular fuzzy numbers, this paper explores a method based on the linear programming model and projection of fuzzy numbers vectors. Some concepts such as the projection of triangular fuzzy numbers vectors, relative degree of approximation, et al, are proposed. Two normalized formula of attribute values are also presented. A linear programming model based on the maximal deviation of weighted attribute values is established, and then the attribute weights are obtained by solving the model. Furthermore, the alterna- tives are ranked by using the projection of the weighted attribute values of every alternative on the fuzzy positive ideal point of alternatives and the fuzzy negative ideal point of alternatives. A numerical example is illustrated to show the feasibility and effectivity of the developed model and method.