Total utility of Z-number

Z-numbers, combined with "constraint" and "reliability", has more power to express human knowledge. How to determine the ordering of Z-numbers and how to make a decision with Z-numbers are both meaningful and open issues. In this paper, a new notion of the total utility of Z-number is proposed to measure the total effects of a Z-number. The proposed total utility of Z-number can be used to determine the ordering of Z-numbers, and can also be simply applied in the application of multi-criteria decision making under uncertain environments. Two particular cases of Z-number (Gaussian and triangular), and some mathematical properties of the total utility of Z-number are discussed in this paper. Several applications and comparative analyses are shown to demonstrate the effectiveness of the proposed total utility of Z-number in the application of ordering Z-numbers and multi-criteria decision making.