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

like p and negation of p. The results of the reasoning process considered in
this chapter differ from that of McDermott's logic [25] on the following
considerations. In McDermott's logic, there exists two stable points in a
system represented by p→ ¬q, and q→¬p, whereas the present method leads
to only one stable point, involving either p or q, depending on the initial fuzzy
beliefs of p, q and their supporting evidences.
Exercises
1. For the FPN given in fig. 10.3, identify the P, Q, P / fm, Q / fm matrices.
Assuming that the relational matrices associated with the transitions to be
the identity matrix and an arbitrary belief vector N(0), compute N(2) by
an appropriate forward reasoning model. What guideline should you
suggest to identify the appropriate reasoning model for a given FPN?
2. Identify the cycle in the FPN of fig. 10.6 by using the algorithm for cycle
detection.
3. From the given belief vectors n5 and n7 in the FPN of fig. 10.8, determine
the belief vectors n1 and n2 by using the backward reasoning algorithm.
Assume that the relational matrices are I.
4. Prove that for a purely cyclic net (P o Q) k = I when k = number of
transitions in the cycle.
5. Given that pre- and post-inverse of matrix I is I. Hence show that
reciprocity relations hold perfectly for a purely cyclic net. Also show that
Rfm and Rbm for such net = I.
6. Prove logically that a dual net can always be constructed by reversing the
arrowheads in a primal net.
7. Can you devise an alternative formulation of the fuzzy inversion of
matrices? [open ended problem]
8. Does the algorithm for computing fuzzy inverse apply to binary matrices?
If yes, can you use it for diagnostic applications in switching circuits?
[open ended problem] [32]-[33].