Using the Dempster‐Shafer orthogonal sum for reasoning which involves space

Abstract

The Dempster‐Shafer theory of evidence gives a solid basis for reasoning about situations characterized by uncertainty. A key feature of the theory is that propositions are represented as subsets of a set which is called a hypothesis space. This power set along with the set operations is a Boolean algebra. The theory has previously been shown to cover other Boolean algebras including collections of objects such as propositions. The practical advantages of this generalization are that increased flexibility of representation is allowed and that the performance of evidence accumulation can be enhanced. The objects of interest here are geometric forms, and we can encode rectangular and other shaped forms using hexadecimal numbers according to shapes and positions. Boolean algebra of such shapes can then be used directly in evidential reasoning exercised. Discusses how medical and other fields can gain from this approach.