A Study of Associative Evidential Reasoning

Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and idempotents and their roles in determining binary operations on intervals of reals are discussed. The appropriate way of constructing formulas for combining evidence and their limitations, for instance, in robustness, are presented.

Evidence Combination and Reasoning and Its Application to Real-World Problem-Solving

In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each other (dependent evidences) or conflicting in supports (conflicting evidences). First, assuming independent evidences, we propose a methodology to construct combination rules which obey a set of essential properties. The method is based on a geometric model. We compare results obtained from Dempster-Shafer's rule and the proposed combination rules with both conflicting and non-conflicting data and show that the values generated by proposed combining rules are in tune with our intuition in both cases. Secondly, in the case that evidences are known to be dependent, we consider extensions of the rules derived for handling conflicting evidence. The performance of proposed rules are shown by different examples. The results show that the proposed rules reasonably make decision under dependent evidences