GENERATED NECESSITIES AND POSSIBILITIES

A necessity measure is a function n from a Boolean algebra B to the real interval [0,1] such that n(x AND y) = min{n(x),n(y)} for every x,y is-an-element-of B and n(0) = 0, n(1) = 1. Necessities are strictly related to Shafer's consonant belief functions and are basic tools when dealing with imprecision and uncertainty. In this article we propose a technique to generate necessities given a collection of items of information quantified by an initial valuation. The method we employ enables us to define conditional necessities in a very natural way and the composition of two necessities by a rule analogous to Dempster's rule. This is obtained by skipping the condition n(0) = 0 and therefore considering necessities with a nonzero "degree of inconsistency."