一种基于图论和直觉模糊偏好关系的准则权重求解方法  

A Method for Deriving Criteria Weights Based on Graph and Intuitionistic Fuzzy Preference Relations

作　　者：牟琼[1,2] 徐泽水[2] 

机构地区：[1]重庆邮电大学应用数学研究所,重庆400065 [2]四川大学商学院,成都610064

出　　处：《系统科学与数学》2017年第4期1049-1062,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(71571123;11671001);长江学者科研经费项目(YJ201430);重庆市科委自然科学基金(cstc2015jcyjA00015;cstc2015jcyjA00034);重庆市教委(KJ1600425)资助课题

摘　　要：直觉模糊偏好关系是处理复杂的多目标群决策间题非常有效的一种工具,其元素可通过对准则集内的所有准则实施两两比较确定.文章在已有的直觉模糊偏好关系的积性一致性和BWM方法的基础上,给出一个新的一致性定义,基于此定义提出一种新的基于图论并从直觉模糊偏好关系中导出准则权重的直觉模糊BWM方法.方法分为三个步骤:第一步,邀请专家组根据对称标度对准则集内的准则进行两两比较,给出每个专家的直觉模糊偏好关系,然后,用简化的直觉模糊加权几何算子将所有专家给出的直觉模糊偏好关系融合成群体的直觉模糊偏好关系;第二步,基于有向网络图设计一个算法,根据点的出度及入度对所有的准则进行排序,并鉴别出最重要和最不重要的准则,在文章给出的新的一致性定义基础上,建立了几个max-min优化模型,模型求解以实现从直觉模糊偏好关系中导出准则的优先权重;第三步,使用文章定义的一致性比率公式检验直觉模糊偏好关系的一致性程度以及所导出权重的可靠性;最后,将直觉模糊BWM决策方法运用于解决实际决策问题,探讨了一个评估医院门诊预约系统的例子,评估结果可以为医疗服务部门和需要进行门诊预约的患者提供决策参考.Intuitionistic fuzzy preference relation （IFPR） is a very efficient tool in tackling comprehensive multi-criteria group decision making problems via pairwise comparisons. Based on the multiplicatively consistent definition of the intuitionistic fuzzy preference relations and the best-worst method （BWM）, according to a symmetrical scale, this paper proposes a novel graph-based approach called the intuitionistic fuzzy best-worst method （IF-BWM）, which can be used to derive the weights of the criteria from IFPRs. To achieve this goal, we first fuse the individual IFPRs provided by the experts into a collective IFPR by the simple intuitionistic fuzzy weighted geometric （SIFWG） operator. Afterwards, we draw the directed network according to the collective IFPR, and then design an algorithm to identify the best and worst criteria through computing the out-degrees and in-degrees of the directed network. Furthermore, we develop some mathematical models corresponding to the definition of the consistent IFPR to derive the weights of criteria, and the consistency ratio can help us to check the effectiveness of the derived weights. Finally, to apply IF-BWM into decision-making problems, a practical application about the effect of clinical appointment registration systems is given, which can help both the medical service and the patients to improve efficiency and provide the best alternative.

关 键 词：直觉模糊偏好关系 一致性 一致性比率 权重 门诊预约 

分 类 号：C934[经济管理—管理学]