There is described a problem of decision making under overabundance of information available from a system of distributed databases, when most of information being relevant to the users' expectations does not fully satisfy other information quality requirements. It is assumed that a preliminary selection of available information improving its quality is connected with a cost and the information users must decide when the selection process should be continued or stopped. The methods of preliminary information selection are discussed and illustrated by examples concerning selection of car selling offers, one of the practical problem solving strategies, and the third one of searching synthetic information characterising a large population of objects. In the first case a stop-rule for the selection process is described, in the second one - a method of strategies assessment based on semi-ordering relations is proposed.
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