Fast Projection of Focal Sets

The efficiency of computations in Dempster-Shafer theory depends crucially on the encoding of focal sets. Most notably, an adequate encoding should allow to compute rapidly the projection, extension and intersection of focal sets. An encoding which has been proposed for that purpose is the binary representation of focal sets. One of its advantages is that the corresponding algorithms can easily be implemented in every high-level programming language which supports arbitrary long integer numbers. In this article, we take a closer look at the binary representation of focal sets. Primarily, our focus of interest is on the projection operation. We give a new implementation which is an order of magnitude faster than previous implementations of the projection operation. A series of empirical tests underline this finding which signifies a significant performance boost of belief function computations.