Dempster-Shafer theory is a special case of vague sets theory

An interesting conclusion is drawn that Dempster -Shafer (DS) theory is a special case of vague set theory: DS theory shares the similar form in the fundamental definition of the measure of a proposition to that in the definition of grade membership of an element in a vague set, and when the elements in a vague set are concretized to be subsets of a total set and the grade membership of the subsets are redefined according to those of DS theory, the vague set becomes DS theory. So some useful conclusions of vague sets hold true in the DS theory when the grade membership of elements take the form of those in DS theory in the research of uncertainty and ignorance.