一种不确定型多属性决策方法及其应用

 讨论了权重完全未知且属性值为区间数的多属性决策问题，提出了一种基于理想区间数贴近度的决策方法。首先定义区间数的距离，并给出区间数贴近度的公理化定义，讨论区间数贴近度的性质，然后针对区间型多属性决策问题给出一种区间型决策矩阵的规范化方法，并给出3种确定权重的方法，分别是模糊标度重心赋权法（主观赋权法）、基于最小相对熵原理的熵与相对熵综合赋权法（客观赋权法）以及利用优化方法，以待评方案与理想最优方案的贴近度最大化为优化目标，建立的贴近度最大化赋权法（主、客观组合赋权法）。利用权重可计算出每个方案与理想方案的综合贴近度，即可得到所有方案的排序结果。最后通过实例分析验证了该方法的有效性和实用性。

A Method for Uncertain Multi-attribute Decision Making and Its Application

This paper studies a kind of decision making problems of uncertain multiple attributes with attribute weights completely unknown and the attribute values being interval numbers. A decision making method based on similarity degree of ideal interval number is proposed. Firstly, the distance of interval number is defined. An axiomatic definition of the interval number similarity degree is given and its properties are discussed. Then, some formulas are derived for normalizing the decision matrix with interval numbers for multiple attribute decision making with intervals. Three methods used to determine the weights are presented, namely, the fuzzy scale center of gravity weighting approach, which is a subjective weight determination; the comprehensive weighting method of entropy and relative entropy, which is an objective weighting approach based on the principle of the minimum relative information entropy; and that by using optimization theory for maximizing similarity degree with similarity degree of project being evaluated to establish the ideal optimization scheme, which is an objective and subjective combined approach to determine weights with better accuracy of the index weight. The comprehensive similarity degree to the ideal solution is calculated to compare all alternatives. Finally, an illustrative example is given to demonstrate the feasibility and practicability of the method.