Attribute Reduction of Crisp-Crisp Concept Lattices Based on Three-Way Decisions.

knowledge reduction in fuzzy environments is a key and difficult issue in data mining and knowledge discovery, the crisp-crisp variable threshold concept lattice is one kind of the knowledge structures in formal fuzzy contexts. The focus of this paper is on the attribute reduction of the crisp-crisp variable threshold concept lattices, the attribute reduction is related to a method of three-way decision based on the crisp-crisp concepts. Firstly, by an illustrating example, we show the extraction of three-way decision rules. A lot of the decision rules are redundant, in order to simplify the nonredundant decision rules and keep their performance invariant, we present a notion of the attribute reduction of formal fuzzy contexts, then we investigate the properties of the attribute redection. Subsequently, with reference to the rough sets, the discernibility matrix and discernibility function of formal fuzzy contexts are presented, so that all the reducts of a formal fuzzy context can be calculated.