This paper derives a new mathematical formula for the combination of a class of belief functions based on Dempster's rule of combination of belief functions. This class of belief functions, which have only singletons and the frame Theta itself as their focal elements, are widely used in possibility theory and rule-inference networks. The mathematical expression developed in this paper enables us to sufficiently compute the combination of belief functions. This paper also deduces the derivatives of combinational belief function w.r.t. all its parameters in case we consider the basic probability assignments as variable parameters. The derivative of combinational belief function provides us a basis to derive learning algorithms for using evidence inference theory in neural networks. This approach has been successfully applied in one of our projects, fuzzy rule networks for identification.
