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

n1,n2
0.8
0.6
0.4
n2
0.1
1 2 4
Shared hours of fun →
n5*,n7*
1 2 4
No. of precedence of murder →
Fig. 10.9(a): Initial belief distribution Fig. 10.9(b): Steady-state distribution
of n1 and n2. of n5 and n7, denoted by
n5*, n7*.
The worst case time complexity of the Procedure Forward reasoning and
Procedure Reducenet are O (m ) and O (a . n ) respectively, where 'm' , 'n' and
'a' denote the number of transitions, number of places before reduction of the
network and number of axioms respectively.
Example 10.4: In the FPN (fig. 10.8) the fuzzy belief distribution
corresponding to places p1 and p2 is shown in fig. 10.9(a). The initial belief
distribution of all other places are null vectors. Further, we assumed R = I.
The steady-state belief distribution at all places in the entire FPN is obtained
after 5 iterations using forward reasoning algorithm, and their distributions at
places p5 and p7 are shown in fig. 10.9(b). Since for all components, n7 is
larger than n5, p7 is marked as the concluding place and then Procedure
reducenet is invoked for tracing explanation for the problem.
10.5 Backward Reasoning in FPN
n1
'Backward reasoning ' [33] in fuzzy logic is concerned with inferring the
membership distribution of the antecedent clauses, when the if-then rule and
the observed distribution of the consequents are available. For example, given
the rule and the observed consequent clause, the inference follows.
Rule: If x-is-A AND y-is-B THEN z-is-C
Observed evidence: z-is-C'
------------------------------------------
Inferred: x-is-A' AND y-is-B'
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0.8
0.5
0.2
0.1
n5*
n7*