权重信息完全未知的二维二元语义多属性群决策方法

针对群决策问题中专家权重和属性权重均未知的情形,提出一种基于二维二元语义表示模型的多属性群决策方法.首先,考虑到不同决策者对二维二元语义信息中第一维信息和第二维信息的相对重要性比重不同,提出一种能够反映出该比重变化对于二维二元语义间比较和距离测度影响的得分函数和距离公式;其次,利用得分函数和距离公式建立目标函数,依据专家意见的熵值确立约束条件,进而构建能够同时求解出专家权重和属性权重的双权重求解模型,再分别针对不同的方案依次进行求解,得到每一个方案假定为最优方案时相应的权重信息;再次,按照所提出的新方法,综合目标函数值的大小对方案进行排序与择优;最后,通过案例分析与对比验证所提方法的有效性和科学性.

A method for multiple attribute group decision making with complete unknown weight information based on 2-dimension 2-tuple linguistic information

Aiming at the situation that the weights of decision makers and criteria are both unknown in group decision making progress, we propose a liner method of multi-attribute decision making based on 2-dimension 2-tuple linguistic representation model. Considering the relative importance of the first dimensional information and the second dimensional information of 2-dimension 2-tuple linguistic information, the score function and distance measures, which can reflect the impact of the change of the proportion of the relative importance on the score function for comparing two 2-dimension 2-tuple linguistic information and distance measures between them, are proposed. Then, decision makers'' weight and criteria weight are solved simultaneously by constructing a model that the objective function is set up based on the score function and distance measures, and constraint conditions are established based on the entropy value of decision makers. Furthermore, the corresponding weights information which makes each alternative optimal is obtained by solving different models, then the optimal alternative and rank alternatives are chosen according to the value of the objective function. Finally, the case analysis and comparison verify the effectiveness and scientificalness of the proposed method.