A multi-level conceptual data reduction approach based on the Lukasiewicz implication

Starting from fuzzy binary data represented as tables in the fuzzy relational database, in this paper, we use fuzzy formal concept analysis to reduce the tables size to only keep the minimal rows in each table, without losing knowledge (i.e., association rules extracted from reduced databases are identical at given precision level). More specifically, we develop a fuzzy extension of a previously proposed algorithm for crisp data reduction without loss of knowledge. The fuzzy Galois connection based on the Lukasiewicz implication is mainly used in the definition of the closure operator according to a precision level, which makes data reduction sensitive to the variation of this precision level.