Closed Random Intervals

Abstract

An important practical problem is modeling evidence about real valued variables. Although the general theory developed in the previous chapter applies to this case, it is necessary, for practical reasons, to limit the models to some simple structures. Such a simple structure is given by set-focused hints whose focal sets are closed intervals of real numbers. Random intervals describe two essential aspects of evidence about numbers: an interval expresses the imprecision of the knowledge about a number and the randomness captures the uncertainty about the number, the possibility of different cases. Due to its simplicity this is a very useful model for practical purposes. This chapter is therefore devoted to a study of this class of hints relative to real numbers. Several results in this chapter can be found in Dempster (1968 b), but here the discussion is extended in several respects.