Attribute reduction in fuzzy concept lattices based on the T implication

Attribute reduction in fuzzy concept lattices based on the kind of transitive regular implication operator (T implication in short) is introduced and investigated. We first propose a kind of fuzzy concept lattices by using T   implication in a fuzzy formal context at a level δ∈IT⊆[0,1] with respect to T   implication. Then we introduce the notion of δδ-reducts in a fuzzy formal context and give some equivalent characterizations of δδ-consistent sets to determine δδ-reducts. Based on δδ-reducts, we divide attributes into three types (at a level δδ) and establish some characterization theorems to determine the type of an attribute.