Specifying nonspecific evidence

Abstract

In an earlier article [J. Schubert, "On nonspecific evidence," Int. J. Intell. Syst. 8(6), 711−725 (1993)] we established within Dempster-Shafer theory a criterion function called the metaconflict function. With this criterion we can partition into subsets a set of several pieces of evidence with propositions that are weakly specified in the sense that it may be uncertain to which event a proposition is referring. Each subset in the partitioning is representing a separate event. The metaconflict function was derived as the plausibility that the partitioning is correct when viewing the conflict in Dempster's rule within each subset as a newly constructed piece of metalevel evidence with a proposition giving support against the entire partitioning. In this article we extend the results of the previous article. We will not only find the most plausible subset for each piece of evidence as was done in the earlier article. In addition we will specify each piece of nonspecific evidence, in the sense that we find to which events the proposition might be referring, by finding the plausibility for every subset that this piece of evidence belong to the subset. In doing this we will automatically receive indication that some evidence might be false. We will then develop a new methodology to exploit these newly specified pieces of evidence in a subsequent reasoning process. This will include methods to discount evidence based on their degree of falsity and on their degree of credibility due to a partial specification of affiliation, as well as a refined method to infer the event of each subset.

Managing Decomposed Belief Functions

“…In standard notation is (4) and is (5) A straightforward combination of m 1 and m 2 yields a pseudo belief function (6) without normalization and (7) after normalization. This is an increase of m 1 's support for A from 1/2 to 3/4 and 3/5, respectively, after combination with m 2 .…”

Interval-Valued Degrees of Belief: Applications of Interval Computations to Expert Systems and Intelligent Control

“…takes the largest possible value (Lesh 163 , Bergsten 28,29,30 , Strat 228,229 , Schubert 209,210,211 ).…”

Creating prototypes for fast classification in Dempster-Shafer clustering

“…In [2] we further investigated the consequence of transferring different pieces of evidence between the subsets. This was done by observing changes in conflict when we moved a piece of evidence from one subset to another.…”

“…These prototypes are not assumed to be preclassified outside of this methodology, instead their classification is derived from a previous clustering process [1]. It is quite possible to cluster and thus classify all incoming evidence without any prototypes as has been done in earlier work [1][2][3][4][5]. While the advantage with this approach is obvious, a fast computation time, there is an disadvantage in that future classification will have a correctness that might by less that what would have been possible if all previous evidence was used in the classification process and not only those that was obtained prior to clustering process.…”

“…They form the foundation for the creation of prototypes in Section 3. A more extensive summary of [1][2] is found in [4]. In Section 4 we develop a method for fast classification based on these prototypes.…”