We present an approach to a Genetic Information Retrieval Agent Filter (GIRAF) for documents from the Internet using a genetic algorithm (GA) with fuzzy set genes to learn the user's information needs. The population of chromosomes with fixed length represents such user's preferences. Each chromosome is associated with a fitness that may be considered the system's belief in the hypothesis that the chromosome, as a query, represents the user's information needs. In a chromosome, every gene characterizes documents by a keyword and an associated occurrence frequency, represented by a certain type of a fuzzy subset of the set of positive integers. Based on the user's evaluation of the documents retrieved by the chromosome, compared to the scores computed by the system, the fitness of the chromosomes is adjusted. A prototype of GIRAF has been developed and tested. The results of the test are discussed, and some directions for further works are pointed out.