The arithmetic of multidimensional Z-number

The Z-number has become a new representation of evaluation information because of its superiority in describing reliability measure. Current studies focuses mainly on the unidimensional Z-number like Z = (about 25 min, usually). Studies on multidimensional cases have not been reported. However, because people often describe things from various aspects, using only one aspect of information to describe uncertain events fully is difficult. In this paper, we propose the concept of the multidimensional Z-number, such as ((about 20 miles, about 25 min), usually) to handle complex information. For this purpose, we first define the basic operations of the multidimensional Z-number. We then propose a feasible comparison method. The effectiveness of the proposed method is demonstrated by a series of numerical examples.