▁interval ▁can ▁be ▁defined . ▁This ▁interval ▁contains ▁the ▁precise ▁probability ▁of ▁a ▁set ▁of ▁interest ▁( in ▁the ▁classical ▁sense ), ▁and ▁is ▁bounded ▁by ▁two ▁non - add itive ▁continuous ▁measures ▁called ▁belief ▁( or ▁support ) ▁and ▁pla us ibility : ▁ ▁The ▁belief ▁bel ( A ) ▁for ▁a ▁set ▁A ▁is ▁defined ▁as ▁the ▁sum ▁of ▁all ▁the ▁masses ▁of ▁subsets ▁of ▁the ▁set ▁of ▁interest : ▁ ▁The ▁pla us ibility ▁pl ( A ) ▁is ▁the ▁sum ▁of ▁all ▁the ▁masses ▁of ▁the ▁sets ▁B ▁that ▁intersect ▁the ▁set ▁of ▁interest ▁A : ▁ ▁The ▁two ▁measures ▁are ▁related ▁to ▁each ▁other ▁as ▁follows : ▁ ▁And ▁convers ely , ▁for ▁finite ▁A , ▁given ▁the ▁belief ▁measure ▁bel ( B ) ▁for ▁all ▁subsets ▁B ▁of ▁A , ▁we ▁can ▁find ▁the ▁masses ▁m ( A ) ▁with ▁the ▁following ▁inverse ▁function : ▁ ▁where ▁| A   −   B | ▁is ▁the ▁difference ▁of ▁the ▁cardinal ities ▁of ▁the ▁two ▁sets . ▁ ▁It ▁follows ▁from ▁the ▁last ▁two ▁equations ▁that , ▁for ▁a ▁finite ▁set ▁X , ▁one ▁needs ▁to ▁know ▁only ▁one ▁of ▁the ▁three ▁( mass , ▁belief , ▁or ▁pla us ibility ) ▁to ▁dedu ce ▁the ▁other ▁two ; ▁though ▁one ▁may ▁need ▁to ▁know ▁the ▁values ▁for ▁many ▁sets ▁in ▁order ▁to ▁calculate ▁one ▁of ▁the ▁other ▁values ▁for ▁a ▁particular ▁set . ▁In ▁the ▁case ▁of ▁an ▁infinite ▁X , ▁there ▁can ▁be ▁well - defined