Abstract This paper presents a new consistency definition of interval multiplicative preference relation (IMPR). Several desirable properties of this new consistency are fully discussed, and the sufficient and necessary conditions of the new consistency definition are also provided. It is proven that this new consistency of IMPR has robustness and invariance with respect to permutation of the compared objects' labels. Moreover, comparative analyses are conducted to reveal the relationships among five existing consistency definitions and this new consistency definition of IMPR. Based on the new consistency definition of IMPR, a new consistency index is introduced to measure the consistency degree of IMPR. An iterative algorithm is proposed to improve the consistency level of an inconsistent IMPR. Subsequently, a goal programming model is built to derive an interval priority vector from an acceptably consistent IMPR. Eventually, a new individual decision making method with an IMPR is put forward. Numerical examples and simulation analyses are conducted to illustrate the superiority and validity of the proposed individual decision making method.

中文翻译：

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区间乘法偏好关系的新一致性定义

摘要 本文提出了区间乘法偏好关系（IMPR）的新一致性定义。充分讨论了这种新一致性的几个理想特性，并提供了新一致性定义的充分必要条件。事实证明，这种新的 IMPR 一致性对于比较对象标签的排列具有鲁棒性和不变性。此外，还进行了比较分析，以揭示五个现有一致性定义与 IMPR 的新一致性定义之间的关系。在新的IMPR一致性定义的基础上，引入了一个新的一致性指标来衡量IMPR的一致性程度。提出了一种迭代算法来提高不一致IMPR的一致性水平。随后，构建目标规划模型以从可接受的一致 IMPR 导出间隔优先级向量。最终，提出了一种新的基于 IMPR 的个体决策方法。数值例子和仿真分析被用来说明所提出的个体决策方法的优越性和有效性。