A Framework for efficient computation of belief theoretic operations

The Dempster-Shafer (DS) theory is a powerful general framework for reasoning under uncertainty. While the strength of the DS theoretic (DST) framework in its ability to handle a wider variety of data imperfections is not in dispute, a major criticism cast towards DST evidential reasoning is the heavy computational burden it entails. If the advantages offered by DS theory is to be fully realized, it is essential that one explores efficient data structures and algorithms that can be used for DST operations and computations. In this paper, we wish to present a novel generalized computational framework for exactly this purpose. We develop three representations - DS-Vector, DS-Matrix, and DS-Tree - which allow DST computation to be performed in significantly less time. These three representations can also be utilized as tools for visualizing DST models. A new strategy, which we refer to as REGAP, which allows REcursive Generation of and Access to Propositions is introduced and harnessed in the development of this framework and computational algorithms. The paper also provides a discussion and experimental validation of the utility, efficiency, and implementation of the proposed data structures and algorithms.