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From: johans@atlas.sto.foa.se (Johan Schubert)
Subject: New Ph.D. thesis in Dempster-Shafer theory available.
Message-ID: <1994Dec5.122245.27645@lin.foa.se>
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Date: Mon, 5 Dec 1994 12:22:45 GMT
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                   Cluster-based Specification Techniques in
                         Dempster-Shafer Theory for an
                      Evidential Intelligence Analysis of
                            Multiple Target Tracks

                                      by

                                Johan Schubert

                         [E-mail: schubert@sto.foa.se]

                   Division of Information System Technology,
              Department of Command and Control Warfare Technology,
                    National Defence Research Establishment,
                          S-172 90  Stockholm, Sweden.


This thesis is based on five articles:
I.   On Nonspecific Evidence, Int. J. Intell. Syst. 8(6), 711-725, 1993.
II.  Specifying Nonspecific Evidence, Manuscript.
III. Finding a Posterior Domain Probability Distribution by Specifying 
     Nonspecific Evidence, Manuscript.
IV.  Dempster's Rule for Evidence Ordered in a Complete Directed Acyclic Graph,
     Int. J. Approx. Reasoning 9(1), 37-73, 1993.
V.   On Rho in a Decision-Theoretic Apparatus of Dempster-Shafer Theory,
     Manuscript.


Abstract

In Intelligence Analysis it is of vital importance to manage uncertainty. 
Intelligence data is almost always uncertain and incomplete, making it
necessary to reason and taking decisions under uncertainty. One way to manage
the uncertainty in Intelligence Analysis is Dempster-Shafer Theory. We may call
this application of Dempster-Shafer Theory "Evidential Intelligence Analysis".
This thesis contains five results regarding multiple target tracks and
intelligence specification in Evidential Intelligence Analysis.
     When simultaneously reasoning with evidence about several different events
it is necessary to separate the evidence according to event. These events
should then be handled independently. However, when propositions of evidences
are weakly specified in the sense that it may not be certain to which
event they are referring, this may not be directly possible. In the first
article of this thesis a criterion for partitioning evidences into subsets
representing events is established.
     In the second article we will specify each piece of nonspecific evidence
by observing changes in cluster and domain conflicts if we move a piece of
evidence from one subset to another. A decrease in cluster conflict is
interpreted as an evidence indicating that this piece of evidence does not
actually belong to the subset where it was placed by the partition. We will
find this kind of evidence regarding the relation between each piece of
evidence and every subset. When this has been done we can make a partial
specification of each piece of evidence.
     In the third article we set out to find a posterior probability
distribution regarding the number of subsets. We use the idea that each single
piece of evidence in a subset supports the existence of that subset. With this
we can create a new bpa that is concerned with the question of how many subsets
we have. In order to obtain the sought-after posterior domain probability
distribution we combine this new bpa with our prior domain probability
distribution.
     For the case of evidence ordered in a complete directed acyclic graph the
fourth article presents a new algorithm with lower computational complexity for
Dempster's rule than that of step by step application of Dempster's rule. We
are interested in finding the most probable completely specified path through
the graph, where transitions are possible only from lower to higher ranked
vertices. The path is here a representation for a sequence of states, for
instance a sequence of snapshots of a physical object's track.
     The fifth article concerns an earlier method for decision making where
expected utility intervals are constructed for different choices. When the
expected utility interval of one alternative is included in that of another, it
is necessary make some assumptions. If there are several different decision
makers we might sometimes be interested in having the highest expected utility
among the decision makers. We must then also take into account the rational 
choices we can assume to be made by later decision makers.

Keywords: Belief functions, Dempster-Shafer theory, evidential reasoning,
          nonspecific evidence, evidence correlation, cluster analysis,
          directed acyclic graph, computational complexity, decision making.


From the Department of Numerical Analysis and Computing Science,
Royal Institute of Technology, Stockholm, Sweden:

TRITA-NA-9410
ISRN KTH/NA/R--94/10--SE
ISSN 0348-2952
ISBN 91-7170-801-4.

Principal advisor: Prof. Stefan Arnborg.
Opponent: Prof. Philippe Smets.




