DEMPSTER COMBINATION RULE FOR SIGNED BELIEF FUNCTIONS

A possibility to define a binary operation over the space of pairs of belief functions, inverse or dual to the well-known Dempster combinati on rule in the same sense in which substraction is dual with respect t o the addition operation in the space of real numbers, can be taken as an important problem for the purely algebraic as well as from the app lication point of view. Or, it offers a way how to eliminate the modif ication of a belief function obtained when combining this original bel ief function with other pieces of information, later proved not to be reliable. In the space of classical belief functions definable by set- valued (generalized) random variables defined on a probability space, the invertibility problem for belief functions, resulting from the abo ve mentioned problem of ''dual'' combination rule, can be proved to be unsolvable up to trivial cases. However, when generalizing the notion of belief functions in such a way that probability space is replaced by more general measurable space with signed measure, inverse belief f unctions can be defined for a large class of belief functions generali zed in the corresponding way. ''Dual'' combination rule is then define d by the application of the Dempster rule to the inverse belief functi ons.