Possibilistic alternatives of elementary notions and relations of the theory of belief functions

summary:The elementary notions and relations of the so called Dempster–Shafer theory, introducing belief functions as the basic numerical characteristic of uncertainty, are modified to the case when probabilistic measures and basic probability assignments are substituted by possibilistic measures and basic possibilistic assignments. It is shown that there exists a high degree of formal similarity between the probabilistic and the possibilistic approaches including the role of the possibilistic Dempster combination rule and the relations concerning the possibilistic nonspecificity degrees

Nonspecificity degrees of basic probability assignments in dempster-shafer theory

Basic probability assignment is a probability distribution on the power-set  (set of all subsets) of a finite set S and the nonspecificity degree of this basic probability assignment is the normalized expected value of the size (cardinality) of subsets of S with respect to this probability distribution. This notion enables to express formally and to prove the intuitive feelings of improving one's basic probability assignment and belief function when combining it with another one by the Dempster combination rule. It enables also to define a basic probability assignment which can be used, at least in certain relations, as an inverse basic probability assignment to the given one with respect to Dempster rule, even if we know that such an inverse element cannot be defined up to the most trivial case of the vacuous basic probability assignment. Analogous properties of the combination rule dual to the Dempster rule are also briefly investigated