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Prioritization and Aggregation of Intuitionistic Preference Relations: A Multiplicative-Transitivity-Based Transformation from Intuitionistic Judgment Data to Priority Weights

机译：直觉偏好关系的优先级排序和聚集：从直觉判断数据到优先权重的基于乘和性的转换

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摘要

This article proposes a goal programming framework for deriving intuitionistic fuzzy weights from intuitionistic preference relations (IPRs). A new multiplicative transitivity is put forward to define consistent IPRs. By analyzing the relationship between intuitionistic fuzzy weights and multiplicative consistency, a transformation formula is introduced to convert normalized intuitionistic fuzzy weights into multiplicative consistent IPRs. By minimizing the absolute deviation between the original judgment and the converted multiplicative consistent IPR, two linear goal programming models are developed to obtain intuitionistic fuzzy weights from IPRs for both individual and group decisions. In the context of multicriteria decision making with a hierarchical structure, a linear program is established to obtain a unified criterion weight vector, which is then used to aggregate local intuitionistic fuzzy weights into global priority weights for final alternative ranking. Two numerical examples are furnished to show the validity and applicability of the proposed models.
机译：本文提出了一种目标规划框架，用于从直觉偏好关系（IPR）导出直觉模糊权重。提出了一种新的乘性传递性来定义一致的IPR。通过分析直觉模糊权重与乘性一致性之间的关系，提出了一种转换公式，将归一化的直觉模糊权重转换为乘性一致性IPR。通过最小化原始判断和转换后的乘性一致IPR之间的绝对偏差，开发了两个线性目标规划模型，以从IPR获得直觉模糊权重，以进行个体决策和群体决策。在具有分层结构的多准则决策的情况下，建立线性程序以获得统一的准则权向量，然后将其用于将局部直觉模糊权重聚合为全局优先权权重，以进行最终替代排序。提供了两个数值示例来说明所提出模型的有效性和适用性。

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