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.