Open AccessA Method of Uncertainty Measurements for Multidimensional Z-number and Their Applications
Author(s) -
Yanfei Li,
Tao Wu,
Junjun Mao,
Haiyan Guo,
Aiting Yao
Publication year - 2020
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2020/8407830
Subject(s) - topsis , entropy (arrow of time) , mathematics , multidimensional analysis , measure (data warehouse) , multidimensional systems , multidimensional data , reliability (semiconductor) , computer science , algorithm , data mining , statistics , operations research , mathematical analysis , power (physics) , physics , quantum mechanics
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.