Basic concepts, definitions, and methods in D number theory

Although DST has many advantages in representing and dealing with uncertainty, but it is limited by some hypotheses and constraints that are hardly satisfied in some situation [3-6]. There are two main aspects. First, in DST a frame of discernment (FOD) must be composed of mutually exclusive elements, which is called the FOD's exclusiveness hypothesis. Second, in DST the sum of basic probabilities or belief m(.) in a basic probability assignment (BPA) must be 1 (or basic probabilities can not be assigned to elements outside the FOD), which is called the BPA's completeness constraint. To overcome the above-mentioned limitations in DST, a new generalization of DST, called D number theory (DNT), has been proposed in recently [7, 8] for the fusion of uncertain information with non-exclusiveness and incompleteness. The theory of DNT stems from the concept of D numbers [9-16], and aims to build a more sophisticated framework for representing and reasoning with uncertain information similar to DST from a generic setmembership perspective, in which DNT relaxes the exclusiveness constraint of elements in FOD and completeness assumption of BPA in DST.