  Dempster-Shafer theory is widely applied in uncertainty modelling and
knowledge reasoning due to its ability of expressing uncertain information. A
distance between two basic probability assignments(BPAs) presents a measure of
performance for identification algorithms based on the evidential theory of
Dempster-Shafer. However, some conditions lead to limitations in practical
application for Dempster-Shafer theory, such as exclusiveness hypothesis and
completeness constraint. To overcome these shortcomings, a novel theory called
D numbers theory is proposed. A distance function of D numbers is proposed to
measure the distance between two D numbers. The distance function of D numbers
is an generalization of distance between two BPAs, which inherits the advantage
of Dempster-Shafer theory and strengthens the capability of uncertainty
modeling. An illustrative case is provided to demonstrate the effectiveness of
the proposed function.
