Certainty Factors in Rule-Based Systems

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 knowledge.

The manipulation of uncertain knowledge in the Rule-based expert systems is illustrated in the next three slide before moving to Bayesian Networks.

Rule Based Systems

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Rule based systems have been discussed in previous lectures.

Here it is recalled to explain uncertainty.

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 assertion.

Example : Trouble shooting of water pumps

If pump failure then the pressure is low

If pump failure then check oil level

If power 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 the domain.

Rules draw conclusions and points to actions, when specific information about the domain comes in. This is called inference.

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 oil level.

â–  It is very difficult to control such a mixture of inference back and forth in the same session and resolve such uncertainties.

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 conclusion.

In its simplest form, this looks like :

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 :

Adding certainty factors.

Adoptions of Dempster-Shafer belief functions.

Inclusion 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).