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

• DOI: 10.1016/j.engappai.2015.06.004
• Publication Date: 2015-06-27T19:50:29Z
• Authors: Meizhu Li; Yong Hu; Qi Zhang; Yong Deng
• Keywords: Dempster–Shafer theory; Signed distance function; Completeness (order theory)

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. HighlightsA 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.