With the ubiquity of preference relations used in group decision making (GDM), controlling the transitivity of preferences characterized by individual consistency has attracted much attention. However, few previous studies consider ordinal and cardinal consistencies simultaneously and the ordinal consistency is often ignored in consensus reaching process in existing studies. In this study, the conditions of individual ordinal consistency are proved to be equivalent to a series of inequalities, based on which, an optimization model is developed to deal with the ordinal inconsistency problem. In addition, a second optimization model is proposed to address the coexistence of both ordinal and cardinal inconsistencies. A framework is designed to provide a complete strategy for controlling consistency. Such a framework is also generalized to accommodate the consensus problem in GDM. Comparing to the existing consistency improvement approaches, the proposed approach explicitly solves the ordinal consistency problem by an optimization approach. Furthermore, the proposed group consensus model guarantees both ordinal consistency and acceptable cardinal consistency when consensus is achieved. Finally, classical examples with extensive comparisons are conducted to show the effectiveness of the proposed approaches.

随着群体决策（GDM）中普遍使用的偏好关系，控制以个人一致性为特征的偏好的传递性引起了很多关注。然而，很少有先前的研究同时考虑序数和基数的一致性，在现有研究的共识达成过程中序数一致性经常被忽略。在这项研究中，单个序数一致性的条件被证明等效于一系列不等式，在此基础上，开发了一个优化模型来处理序数不一致问题。此外，提出了第二个优化模型来解决序数和基数不一致的共存问题。设计框架是为了提供控制一致性的完整策略。还概括了这种框架，以适应GDM中的共识问题。与现有的一致性改进方法相比，所提出的方法通过优化方法显着解决了序贯一致性问题。此外，当达成共识时，建议的群体共识模型可保证序贯一致性和可接受的基本一致性。最后，对经典示例进行了广泛的比较，以证明所提出方法的有效性。