Fuzzy summarization of data using fuzzy cardinalities

International audienceThe paper investigates the following knowledge extraction method from a database. A set of a small number of attributes of interest are chosen. The idea is to figure out to what extent one of the attributes (the "output attribute" B) is influenced by the others (called "input attributes"Ai). Each of the input attribute domain are supposed to be equipped with a fuzzy partition made of a relatively small number (2 to 5) of fuzzy sets Ai/j or Bk respectively. These fuzzy partitions are supposed to be meaningful for the user and/or to be in agreement with the way the attribute values are scattered. For a given tuple (Alj,..., An/j, Bk), we compute the fuzzy cardinality of the set of items of the database which are A1/j and ... and An/j and Bk , and of the set of item which are A1/j i and...and An/j. From which we can easily obtain the fuzzy-valued confidence and support of the association rule "if x is A1/j, and ... and An/j then x is Bk". In order to obtain more interesting association rules, the Bk are not chosen beforehand, but on the basis of a possibilistic case-based reasoning machinery which provides the fuzzy set of possible output values for a class of situations described in terms of labels Ai/j of the fuzzy partitions of the input attributes. Thus a set of fuzzy association rules summarizing a database can be obtained