犹豫模糊偏好关系一致性改进算法及群决策

Algorithm for Improving the Consistency of Hesitant Fuzzy Preference Relations and Its Group Decision Making

犹豫模糊偏好关系一致性分析方法是群决策问题中的一个重要课题。基于犹豫模糊偏好关系,对加性一致性、一致性指数、满意一致性进行了定义和度量,研究了加性一致性犹豫模糊偏好关系的若干判定条件,构造了满足加性一致性的特征偏好关系。在此基础上,构建了犹豫模糊偏好关系的加性一致性改进算法,论证了算法的收敛性,该算法使得改进后的犹豫模糊偏好关系满足满意一致性条件,进而使得决策者获得合理可靠的决策结果。最后建立了基于犹豫模糊偏好关系加性一致性的群决策模型,并通过应急管理系统的选择实验说明提出的群决策模型是合理的和有效的。

The consistency analysis method of hesitant fuzzy preference relation （HFPR） is an important issue in group decision making （GDM） problems. In view of the HFPRs, the concepts of additive consistency, consistency index and acceptable consistency of HFPRs are introduced. Then, the determination conditions of additive consistent HFPRs are investigated, and the additive consistent characteristic preference relation is constructed. Based on the characteristic preference relation, a convergent consistency-improving algorithm is proposed to adjust unacceptably additive consistent HFPR into an acceptably additive one, and it helps the decision makers to obtain the reasonable and reliable GDM results. Finally, a GDM model is put forward on the base of the additive consistent HFPR. A practical application to selection of emergency management system is demonstrated to show the rationality and effectiveness of the proposed GDM model.