D numbers theory: a generalization of Dempster-Shafer evidence theory
  Efficient modeling of uncertain information in real world is still an open
issue. Dempster-Shafer evidence theory is one of the most commonly used
methods. However, the Dempster-Shafer evidence theory has the assumption that
the hypothesis in the framework of discernment is exclusive of each other. This
condition can be violated in real applications, especially in linguistic
decision making since the linguistic variables are not exclusive of each others
essentially. In this paper, a new theory, called as D numbers theory (DNT), is
systematically developed to address this issue. The combination rule of two D
numbers is presented. An coefficient is defined to measure the exclusive degree
among the hypotheses in the framework of discernment. The combination rule of
two D numbers is presented. If the exclusive coefficient is one which means
that the hypothesis in the framework of discernment is exclusive of each other
totally, the D combination is degenerated as the classical Dempster combination
rule. Finally, a linguistic variables transformation of D numbers is presented
to make a decision. A numerical example on linguistic evidential decision
making is used to illustrate the efficiency of the proposed D numbers theory.
