Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

“If you can manage to evaluate the conditional probabilities, then use
Pearl’s model. If your frame of discernment is small or you can afford to
spend computational time, use the Dempster-Shafer theory. If you are happy
with less accurate but quick results, use fuzzy logic.”
Another important question that may appear to the readers: can we
use any of these models to any problem? The answer depends on whether we
can represent the problem by a given model. Shenoy and Shafer [7] in one of
their recent papers claim that Pearl’s model is a special case of their extended
model of local computations on a qualitative Markov tree. It is thus evident
that both Pearl’s model and the DS theory can perform the problem of data
fusion [2]. But the user has to determine the appropriate data sets required for
solving the problem by any of these methods. The same line of reasoning is
equally valid for fuzzy logic.
Exercises
1. List the set of parameters (conditional probabilities by name) and the
inputs (a priori probabilities and λs at the instantiated leaf node) required
to apply the belief propagation scheme, when node E (in fig. 9.4) is
instantiated at E = E2.
2. After instantiation of node E (in fig. 9.4), compute manually the Bel
values, λ and Π messages at the equilibrium state, based on your initial
assignments. Can you construct a program to realize this?
3. Suppose a crime was committed by either of three suspects A, B, or C.
There are two knowledge sources. The knowledge source 1 submits the
following data:
m1{(A)} = 0.1, m1{(B)}= 0.3, m1{(C)} = 0.3 and m1 {(θ)} = 0.3.
The knowledge source 2 submits the following data:
m2{(A)}= 0.4, m2{(B)} = 0.2, m2{(C)} = 0.2 and m2{(θ)} =0.2.
Find m12{(A)}, m12{(B)} and m12{(C)} and hence comment on the
culprit.
4. Find the relational matrices for the following systems: