Abstract: A multi-criteria fuzzy decision-making method based on interval-valued intuitionistic fuzzy number is proposed for some situations where the information about criteria weights for alternatives is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. The vectors of alternative, ideal and critical alternative are defined. A projection measure method is proposed, in which the attribute values are in the form of interval-valued intuitionistic fuzzy set. A non-linear programming model, based on the Jaynes’ maximum entropy principle and alternatives’ fair competition, is established to obtain the attribute weights. A new relative closeness degree formula based on ideal and critical alternative is presented in order to rank the alternatives. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.

Key words: multiple criteria analysis, interval-valued intuitionistic fuzzy number, bidirectional projection, Jaynes&rsquo, maximum entropy

摘要： 研究了权重不完全确定，评价信息为区间直觉模糊数的多属性决策问题。提出了方案与理想方案、临界方案形成的向量表达方式，建立了针对区间直觉模糊信息的向量投影测度方法；构建了基于Jaynes最大熵原理和方案公平竞争下的非线性规划属性权重确定模型；提出了基于理想方案与临界方案的贴近度测算公式，以此对方案进行排序。通过算例对比分析说明了该方法的有效性和可行性。

关键词: 多属性决策, 区间直觉模糊数, 双向投影, Jaynes最大熵