基于区间二元语义的动态灰色关联群决策方法及应用

Dynamic grey incidence group decision making methodology based on interval two-tuple linguistic information processing and application

在动态群决策中属性值往往为区间语言信息,而数值决策模型难以处理,鉴于此,构建了一种动态灰色关联群决策模型。首先利用区间二元语义信息的运算法则与性质,集结信息评价矩阵;针对时间权重和专家权重已知而属性权重信息完全未知的情形,设计各时间段的正、负理想方案,以与正理想方案灰色关联度偏差最小化为目标构建多目标规划模型,确定属性权重;基于各时间段各方案对正、负理想方案的区间二元语义灰色关联度,构建方案优属度的优化模型,进而获得方案优属度的表达式。最后以案例验证了所提方法的有效性和可行性。结果表明,所提方法能够较为精确地处理语言信息,在一定程度上克服基于以往语言信息处理方法造成的信息扭曲和损失。

With respect to the problem that index value is ofter given in the form of interval linguistic as- sessment information in the dynamic multiple attribute group decision making, a novel dynamic grey incidence group decision making methodology based on interval two-tuple linguistic information is proposed. Firstly, the algorithms and properties of the interval two-tuple linguistic information are used to aggregate the information evaluation matrix. Secondly, the positive and negative ideal schemes for each time period are designed in order to deal with the problem that the expert weights and time weights are known, while index weights are un known, so that the multi-objective programming model with the minimum deviation of the grey incidence degree between each scheme and the positive ideal scheme for each stage is built to determine the index weights. Third ly, the grey incidence each stage degree with interval two-tuple linguistic information between each scheme and the positive and negative ideal scheme for each stage is calculated to establish the optimization model of the opti- mal membership degree for scheme, so that the expressions form of the optimal membership degree for scheme is determined to solve the optimal membership degree for scheme. Finally, an example validates the feasibility and effectiveness of the novel model. The results show that the proposed method can more precisely deal with the language information and avoid information distortion and loss based on the previous method of processing the language.