基于直觉梯形模糊数的灰关联投影寻踪动态聚类多属性决策方法

Grey relation-projection pursuit dynamic cluster method for multiattribute decision making assessment with trapezoidal intuitionistic fuzzy numbers

针对属性权重完全未知,属性值以直觉梯形模糊数形式给出的多属性决策问题,提出一种灰关联投影寻踪动态聚类法.该方法综合考虑灰色关联和优隶属度,改进灰关联投影法(GRPM),并将改进的灰关联投影法与投影寻踪动态聚类(PPDC)方法结合,构建投影目标函数.引入萤火虫算法(FA)优化投影目标函数,寻求灰关联投影值的最佳投影方向,从而求得灰关联投影值.根据灰关联投影值的大小对备选方案进行分类、排序和择优.实例分析结果验证了所提出方法的有效性和可行性.

Aiming at unknown attribute weights and attribute values which are expressed in trapezoidal intuitionistic fuzzy numbers, a gray relation projection pursuit dynamic cluster method is proposed. This method improves grey correlation projection method（GRPM） under the comprehensive consideration of preferential membership and grey correlation, combines projection pursuit dynamic cluster（PPDC） method and the grey relation projection method, and constructs the projection objective function. The firefly algorithm（FA） is adopted to optimize the objective function of projection for obtaining the best projection direction of grey correlation projection values, and the grey correlation projection values are evaluated, which are applied to classify, rank and prefer the alternatives. Results of the application examples verify the effectiveness and feasibility of the proposed method.