Belief Functions Induced by Partial Compatibility Relations

Abstract

A common feature of the following three chapters consists in their aim to go beyond the framework of the already classical mathematical model for Dempster—Shafer theory, as explained and analyzed till now, in at least the three following directions: (i) to weaken the demands imposed to the notion of compatibility relation as the basic relation binding the empirical data being at the user’s (observer’s) disposal with the hypothetical internal states of the system under investigation (this chapter); (ii) to abandon the assumption that the state space S is finite and to extend the definition of degrees of beliefs to at least some subsets of an infinite space S (the next chapter); (iii) to replace the probabilistic measures used in our definitions of basic probability assignments and belief functions by more general set functions, e. g., by measures or signed measures, in order to generalize the notion of basic probability assignment and belief function so that an operation inverse to the Dempster combination rule were definable if not totally, so at least for a large class of generalized basic probability assignments (Chapter 10).