Taking decisions

by Piotr SYNAK, Dominik ŚLĘZAK

Decision problems are certainly among the most interesting and significant problems that have multiple applications in various areas of science as well as in real life. Essentially they consist in finding an answer to the following general question: " Assuming some knowledge on a particular phenomenon, what is the appropriate decision to be taken in a particular moment?" To start with medical problems, this may mean, for example, deducing from an EEG whether a child is epileptic or runs the risk of becoming one. Another example: a complex market analysis aiming at predicting possible changes in the value of some particular stock on the market.

When facing decision problems, you must be aware of the possible difficulties in finding the correct answer. Wrong decisions are usually attributed to non-representative or incomplete knowledge. In fact, properly using the acquired knowledge in order to get a correct classification (correct decision) is no trivial matter at all.

One of the most common ways of knowledge representation is to treat its elements as objects endowed with some attributes. Usually you have to do with data tables, with rows corresponding to objects and columns containing the values of object attributes. One of the columns (attributes) is distinguished from all the other and is assigned to the decision problem. The task consists in finding the dependence between the decision and the other attributes (conditions) by observing known objects. This deduction from partial knowledge is by no means an easy task, be it only because of scarce information about all the essential properties of objects. Therefore the required dependence is often replaced by approximate relations, thus making the entire process more effective. Another problem is due to the fact that available computer power is often insufficient for the treatment of a huge amount of information, as is the case with the two examples quoted above. In such circumstances the hitherto known methods for discovering the dependence fail. One of the possible solutions consists in decomposing huge data tables into smaller parts. Then the problem is reduced to inferring the global state of things from local analysis of smaller samples - and this seems to be closely related to the understanding and translating into a computer language of the intellectual processes of the human being itself.