In human communication, analogical inference plays an important role in forming useful judgements from uncertain and incomplete information. Implementation of such ability of inference in computers is significant to increase the efficiency of the question-answering process in information retrieval systems. A new notion of topological fuzzy sets is introduced to describe analogical inference based on association between concepts quantitatively. Based on the above idea, a question-answering system for information retrieval is proposed where a computer learns users' subjects of interest. In the learning process the computer puts questions so as to reduce the fuzziness of its recognition on the users' subjects. Finally, we implemented the system and, using it, the effect of the analogical inference on the efficiency of the learning is investigated.