ABSTRACT
The theory of belief functions began as an attempt by Dempster to formalize some of Fisher’s fiducial reasoning techniques. The next major development in the theory of belief functions is its integration with graphical models. Kong developed graphical methods for belief functions over large outcome spaces (or frames). This chapter reviews basic belief function definitions over discrete and continuous frames of discernment and two important belief function operations: projection and combination. The mass function plays a very important role in belief function theory: many of the important definitions are in terms of the mass rather than the belief or plausibility. The chapter provides the basic definitions in the discrete case, and introduces models for component failure rates require belief functions defined over continuous frames. It builds a toolkit of belief function operations which form the core of the fusion and propagation algorithm.
