A Method of Uncertainty Measurements for Multidimensional Z-number and Their Applications

Abstract EN

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.