A novel distance function of D numbers and its application in product engineering

• A distance function between two D numbers is proposed and applied in product engineering.
• The function is effective when elements in the frame of discernment aren׳t mutually exclusive.

The 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 of algorithms based on the evidential theory of Dempster–Shafer. However, some conditions lead to limitations in practical application for the 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 a generalization of distance between two BPAs, which inherits the advantage of Dempster–Shafer theory and strengthens the capability of uncertainty modeling. An illustrative case about product engineering is provided to demonstrate the effectiveness of the proposed function.