Z-number provides the reliability of evaluation information, and it is widely used in many fields. However, people usually describe things from various aspects, so multidimensional Z-number has more advantages over traditional Z-number in describing evaluation information. In view of the uncertainty of the multidimensional Z-number, the entropy of multidimensional Z-number is defined and an entropy formula of multidimensional Z-number is established. Furthermore, the entropy is used to construct an average operator of multidimensional Z-numbers. In addition, a novel distance measure is introduced to measure the distance between two multidimensional Z-numbers. Moreover, the group decision model in the multidimensional Z-number environment is constructed by combining the average operator with the TOPSIS decision-making method. Finally, an illustrative example is given to verify the feasibility and effectiveness of the proposed method.
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机译：Z值提供了评估信息的可靠性，在许多领域得到了广泛的应用。然而，人们通常从各个方面来描述事物，因此多维Z数在描述评价信息方面比传统的Z数更具优势。针对多维Z数的不确定性，定义了多维Z数的熵，建立了多维Z数的熵公式。此外，熵用于构造多维 Z 数的平均算子。此外，还引入了一种新的距离度量来测量两个多维Z数之间的距离。此外，将平均算子与TOPSIS决策方法相结合，构建了多维Z数环境下的群决策模型。最后，通过算例验证了所提方法的可行性和有效性。
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