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

of precision of data and certainty of knowledge can be modeled with the
notion of probability, let us consider example 9.1.
Example 9.1: Consider the following production rule PRi.
PRi: { IF (the-observed-evidences-is-rash) (x ),
AND (the-observed-evidences-is-fever) (y),
AND (the-observed-evidences-is-high-pain) (z ),
THEN (the-patient-bears-German-Measles)} (CF )
where x, y, z denote the degree of precision / beliefs / conditional probabilities
that the patient bears a symptom, assuming he has German Measles. On the
other hand, CF represents the degree of certainty of the rule or certainty factor/
probability that the patient bears German Measles, assuming the prior
occurrence of the antecedent clauses. It is, now, clear that the same problem
can be modeled by many of the existing techniques; of course, for the purpose
of reasoning by a technique we need a particular kind of parameter.
9.2.1 Bayesian Reasoning
Under this context, we are supposed to compute P( Hi / Ej ) or P ( Hi / E1, E2,
... Em) where Hi represent a hypothesis and Ej represents observed evidences
where 1 ≤ j ≤ m. With respect to a medical diagnosis problem, let Hi and Ej
denote the i-th disease and j-th symptoms respectively. It is to be noted that
under Bayesian reasoning we have to compute the inverse probability [P (Hi /
Ej )], rather than the original probability, P(Ej /Hi). Before describing the
Bayesian reasoning, let us revise our knowledge on conditional probabilities.
Definition 9.1: Conditional probability [1] P (H / E) is given by
P(H / E) = P(H ∩ E) / P(E) = P(H & E) / P(E),
where H and E are two events and P (H ∩ E) denotes the joint occurrence of
the events H & E. Analogously,
P(E / H) = P(E & H) / P(H) .
Now, since P(E & H) = P(H & E), we find
P(E & H) = P(E / H) . P (H) = P(H / E) . P (E)