Certainty Factors in Rule-Based Systems
The certainty-factor model was one of the most popular model for
the representation and manipulation of uncertain knowledge in the early (1980s)
Rule-based expert systems.
The model was criticized by resea hers in artificial intelligence
and statistics being ad-hoc-in nature. Resea hers and developers have stopped
using the model.
Its place has been taken by more expressive formalisms of
Bayesian belief networks for the representation and manipulation of uncertain
The manipulation of uncertain knowledge in the Rule-based expert
systems is illustrated in the next three slide before moving to Bayesian
Rule Based Systems
Rule based systems have been
discussed in previous lectures.
Here it is recalled to explain
A rule is an expression of the form
"if A then B" where A is an assertion and B can be either an action or another
Example : Trouble shooting of
failure then the pressure is low
failure then check oil level
failure then pump failure
Rule based system consists of a
library of such rules.
Rules reflect essential
relationships within the domain.
Rules reflect ways to reason about
Rules draw conclusions and points
to actions, when specific information about the domain comes in. This is called
The inference is a kind of chain
reaction like :
If there is a power failure then
(see rules 1, 2, 3 mentioned above) Rule 3 states that there is a pump failure, and
Rule 1 tells that the pressure is low, and
Rule 2 gives a (useless) recommendation to check the
â– It is very difficult to control such a mixture of inference
back and forth in the same session and resolve
How to deal such uncertainties ?
How to deal uncertainties in rule based system?
A problem with rule-based systems is that often the connections
reflected by the rules are not absolutely certain (i.e. deterministic), and the
gathered information is often subject to uncertainty.
In such cases, a certainty measure is added to the premises as
well as the conclusions in the rules of the system.
A rule then provides a function that describes : how much a
change in the certainty of the premise will change the certainty of the
In its simplest form, this looks
If A (with certainty x) then B (with certainty f(x))
This is a new rule, say rule 4, added to earlier three rules.
There are many schemes for treating
uncertainty in rule based systems. The most common are :
of Dempster-Shafer belief functions.
of fuzzy logic.
In these schemes, uncertainty is
treated locally, means action is connected directly to incoming rules and
uncertainty of their elements. Example : In addition to rule 4 , in previous
slide, we have the rule
If C (with certainty x) then B (with certainty g(x))
Now If the information is that A holds with certainty a and C
holds with certainty c, Then what is the certainty of B ?
Note : Depending on the scheme,
there are different algebras for such a combination of uncertainty. But all
these algebras in many cases come to incorrect conclusions because combination
of uncertainty is not a local phenomenon, but it is strongly dependent on the
entire situation (in principle a global matter).