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

µfast runner(x)
0.9
0.6
0.2
0.1
5 6 8 10
Speed (m/s)
(c)
Fig. 10.1: Membership distribution of (a) tall(x), (b) stout (x) and
(c) fast runner (x).
With the given set of database and knowledge base, a Petri net (vide
fig.10.2) is now constructed. The algorithm for formation of the Petri net will
be presented shortly. However, before describing the algorithm, let us first
explain the problem under consideration. Assuming that the observed
membership distributions for Tall (ram) and Stout (ram) respectively are
µ tall (ram) = [0.6/5' 0.8/6' 0.9/7' 0.4/8'] T = n1
µ stout (ram) = [0.2/40kg 0.9/50kg 0.6/ 60kg 0.3/80kg] T = n2
and the distribution of all other predicates to be null vectors, one can estimate
steady-state distribution [17] for all predicates. Such estimation requires
updating of FTT distributions t1 and t2 in parallel, followed by updating of
membership distribution at all places in parallel. This is termed a belief
revision cycle [16]. A number of such belief revision cycles may be repeated
until fuzzy temporal membership distributions at the places become either
time-invariant or demonstrate sustained oscillations. Details of these issues
will be covered in section 10.3.
The following parameters in the FPN in fig.10.2 are assumed for
illustration. P = {p1, p2, p3, p4}, D = {d1, d2, d3, d4} where d1=Tall (ram),
d2=Stout (ram), d3 = Fast-runner (ram), d4 = Has-nominal-pulse-rate (ram). n1
= [0.6 0.8 0.9 0.4] T , n2 = [0.2 0.9 0.6 0.3] T , n3 = n4= null vector. It may be
added here that these belief vectors [33] are assigned at time t = 0 and may be
updated in each belief revision cycle. It is therefore convenient to include
time as argument of ni's for 1≤i ≤ 4. For example, we could refer to ni at t = 0
by ni (0). Tr set in the present context is Tr = {tr1, tr2}; t1 and t2 are FTT
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