Abstract: The paper mainly researches the multi-attribute group decision making with the preference information in the form of interval number and unknown objective weights of attributes and decision makers, and proposes the comprehensive weights of attributes can be calculated by combining the subjective weights and the objective ones. The objective weights are obtained by the methods of entropy analysis of the deviation degree in the attributes assessment values and establishing the nonlinear programming model of minimal goal. Based on the determining of decision makers’ objective weights, which are obtained by analyzing the consistency between each decision maker’s comprehensive evaluation and group decision makers’ comprehensive evaluation using the gray correlation method, the stable weights of decision makers can be obtained after the adaptive iterative process. A new formula of possibility degree for the interval number comparison is proposed. Based on this formula, the method for dealing with the ranking problems of alternatives is presented. The proposed method is proved to be feasible and effective by the case analysis and comparison with other method. Finally, the influence of related parameters on the decision result is analyzed.

Key words: group decision making, interval number, attributes&rsquo, weights, decision makers&rsquo, weights, probability degree

摘要： 针对偏好信息为区间数形式、属性和专家客观权重未知的多属性群决策问题，提出通过属性评价值之间偏离程度的熵值分析和建立目标最小化的非线性规划模型确定属性客观权重，并结合属性主观权重获得属性综合权重；通过灰色关联法分析专家综合评价和群体综合评价之间一致性程度确定专家客观权重，并利用自适应迭代法求得稳定的专家权重；构造了一个新的区间数比较的可能度公式，并基于此公式，给出了方案排序问题的解决方法。通过算例分析及与其他方法对比，验证了所提出方法的可行性和有效性。最后，分析了相关参数对决策结果的影响。

关键词: 群决策, 区间数, 属性权重, 专家权重, 可能度