Normalized projection approach to group decision-making with hybrid decision information

  • Chuan YueEmail author
Original Article


Projection is an important measure in decision science, and it is also often used as a tool for various administrators. However, there are some defects in the existing projection models. To solve this significant scientific problem, this paper intends to establish new projection measures between two real vectors and between two interval vectors. First, the hidden flaws of existing projection measures are pertinently shown, and new projection measures in real number and interval settings are established, which satisfy the condition of normalization. Then new projection measures are applied to group decision-making with hybrid decision information, including real numbers and interval data. Finally, an experimental analysis shows the applicability, feasibility, effectiveness and advantages of the proposed methods.


Normalized projection measure Group decision-making Interval data Hybrid decision information 



The author would like to thank the editors and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to this improved version of the paper. This work was partially supported by the Education and Teaching Reform Program of Guangdong Ocean University (XJG201644).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Mathematics and Computer ScienceGuangdong Ocean UniversityZhanjiangChina

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