Page 410 - Introduction to AI Robotics

11.4 Dempster-Shafer Theory
1.0 393

don’t know Empty = Empty don’t know U
don’t know
U
don’t know
= don’t know
Bel 0.6 X 0. 6 = 0.36 0.6 X 0. 4 = 0.24
1
0.4
don’t know U
occupied Occupied = φ U Empty = Occupied
Occupied

0.4 X 0. 6 = 0.24 0.4 X 0. 4 = 0.16
0.0
empty don’t know
0.0 0.6 1.0
Bel
2

Figure 11.7 Example of the need for normalization.

belief. For the previous example the total area of valid belief was 1.0, so the
belief for a set was computed as:

P
(m(C k )
m(C) k =
1:0
If a portion of that area belongs to ; (or there are p areas for ;), then the
total area is 1:0 m(;):

P (m(C k )
m(C) k P =
1 m(; p )
p
Normalizing leads to:

m(O ) = 0:16 = 0:21
ccupied
1 0:24
m(E ) = 0:36 = 0:47
mpty
1 0:24
m(dontknow ) = 0:24 = 0:32
1 0:24
This idea of summing up the areas for a particular proposition and nor-
malizing can be captured with a mathematical formula known as Dempster’s