## Qualitative Modelling And Its Applications - A Survey

**Gyula Roman, Gyula Tomossy**
Department of Measurement and Instrumentation Engineering

Technical University of Budapest

H-1521 Budapest, Hungary

E-mail: roman@mmt.bme.hu

Modelling always played a key role in problem solving. Traditionally
models were based on differential equations, and the solution
to the problems was sought by explicitely solving the equations.
With the technical development the complexity of the problems
increased significantly and the traditional models often become
excessively complex to be handled within reasonable time limits.
On the other hand, we very often aim at problems poorly described
where traditional methods lack sufficient information to lead
to useful solutions (such methods are operational only if complete
information is provided).

In these situations a different modelling approach - qualitative
modelling - offers a solution. In qualitative modelling values
of model variables are taken from a discrete set which represent
the significant points - landmarks - in the domain of the variable.

Although this domain reduction is very useful, the main power
lies in abstracting the mathematical relations themselves. In
qualitative modelling this further step is also taken; the exact
well defined mathematical functions and relations are mapped to
their qualitative counterparts. With this approach we can extract
useful information from an analytically poorly described model.

However, we have to make sacrifice for such flexibility: the
solutions are also qualitative. A more serious problem, invalid
"spurious" solutions are also generated. To cope with
it, more and more information is condensed into the qualitative
values. Some approaches introduced intervals as means of extended
information, others utilized fuzzy sets.

The goal of this paper is to present an overview of qualitative
modelling, and to demonstrate with specific examples the power
of this approach in the typical engineering problems.