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

The orthogonal summation operations of more than two belief functions can
be computed in an analogous manner, by taking two belief functions, one at a
time. The major drawback of this technique is high time-complexity, which in
the worst case may be as high as p1 x p2, where p1 and p2 represent the
hypothesis space of the two sources of evidences. Thus for combining belief
from n sources, the overall time-complexity in the worst case is p1 x p2 x....
pn, where pi represents the number of hypothesis in the i-th knowledge source.
Summarizing, the above concept, the worst case time-complexity for n
composition of beliefs from n sources is O (p n ), where p1 = p2 =.... pn = p,
say. This exponential time-complexity can be reduced [7], by performing
belief combinations on local families, instead of combining beliefs on the
entire frames.
9.3 Certainty Factor Based Reasoning
The Bayesian reasoning technique, though successfully applied in many areas
of science and technology, is not appropriate for applications in the domain
of problems, where the hypotheses are not mutually exclusive. An alternative
technique for evidential reasoning was, therefore, needed to meet the
crisis. In the early 1970’s, a new technique based on certainty factors was
developed under the aegis of the Heuristic Programming Project of
Stanford University [9], [11]. The context was the development of
computer-based medical consultation systems and in particular the MYCIN
project [94 ] which was concerned with replicating a consultant in the antimicrobial
therapy.
‘Certainty factor’ (CF) in the treatises [9-10] was considered to be
associated with a given priori hypothesis. This factor ranges from -1,
representing the statement ‘believed to be wholly untrue’, to +1, representing
the statement ‘believed to be wholly true’. Further, there is no assumption
like ∑ CF ( i ) = 1 for i= 1 to n, where n is the number of the
hypotheses. Thus the method is not in any sense probabilistic in its origin or
basis. The CF itself is computed as the difference between two measures:
the current measure of belief (MB) and the current measure of disbelief
(MD):
CF (H : E ) = MB (H : E ) - MD (H : E)
for each hypothesis H, given evidence E.