D numbers theory: a generalization of Dempster-Shafer theory

Dempster-Shafer theory is widely applied to uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. However, some conditions, such as exclusiveness hypothesis and completeness constraint, limit its development and application to a large extend. To overcome these shortcomings in Dempster-Shafer theory and enhance its capability of representing uncertain information, a novel theory called D numbers theory is systematically proposed in this paper. Within the proposed theory, uncertain information is expressed by D numbers, reasoning and synthesization of information are implemented by D numbers combination rule. The proposed D numbers theory is an generalization of Dempster-Shafer theory, which inherits the advantage of Dempster-Shafer theory and strengthens its capability of uncertainty modelling.