Page 193 - DCAP506_ARTIFICIAL_INTELLIGENCE

Unit 13: Expert Systems and its Architecture

13.8 Dealing with Uncertainty Notes

The description of knowledge is quite vague and imprecise, and includes a great deal of
Uncertainty. There are many mathematical theories for expressing uncertainty and which could
be used to deal with the uncertainty in the description of the user knowledge. We decided to use
fuzzy set theory (Zadeh, 1965): the user model representation is based on fuzzy sets and model
updating on fuzzy rules (Kavcic, 2001).

13.8.1 Domain Knowledge Representation

There are two types of relations between domain concepts. The essential prerequisite relation
can exist between two concepts only to some extend; therefore we describe it as a fuzzy relation
(Kavcic, 2001). The supportive prerequisite relation is always fully present (if it is present at all)
and is therefore described as a normal crisp relation. Since the essential prerequisite relation is
defined as a fuzzy relation, the domain concept graph is also a fuzzy structure.

13.8.2 User Knowledge Representation

The domain knowledge representation is also used for describing user knowledge, which is a
subset of the domain knowledge. An overlay over the domain model is used, so the user model
can be regarded as a sub graph of the domain concept graph. Each concept of the sub graph has
some additional properties attached, which explain the user knowledge of this concept: a triple
of membership functions for three fuzzy sets of unknown, known and learned concepts. As a
result, a fuzzy graph with fuzzy relations and fuzzy nodes is a base for user knowledge
representation (Kavcic, 2001).

13.8.3 Knowledge Determination and Updating

The user knowledge of domain concepts changes (increases) during the interaction with the
system. Consequently, the user model also changes to reflect the current user understanding of
the teaching domain. The main principle for gathering information about the user knowledge is
checking tests results and analyzing learning units that the user visits. If the user knowledge
changes through user actions, it always increases. Even when the user performs poorly, it never
decreases.

13.8.4 Model Initialization

The user model is initialized using the results of a quick pre-test, which each new user is
required to solve. During this initialization, each domain concept becomes either fully learned
or remains completely unknown.

13.8.5 Model Updating

The most significant changes in user knowledge of the domain can be recorded when the user
answers the test questions corresponding to a certain learning unit. Tests are used for checking
how well a particular concept is learned and a set of corresponding test questions is provided for
each learning unit. After the user successfully solves the test on one domain concept, the
membership value for a set of learned concepts is increased for this concept, regardless of the
previous knowledge level of this particular concept. If the test questions are not answered
satisfactory, the value does not change. We also update the user model after each visit of a
learning unit; especially first visits of units and visits of still not learned units have the biggest

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