Crisp-Fuzzy Concept Lattice Based on Interval-Valued Fuzzy Sets

Fuzzy concept lattices can be viewed as the generalizations of the classical concept lattices in fuzzy formal contexts, which is a key issue and a major research direction in knowledge discovery. Crisp-fuzzy concept lattices are special fuzzy concept lattices, the existing crisp-fuzzy concept lattices can be divided into two categories, that is, one is the extension of the classical concept lattice, and the other is based on rough fuzzy approximation operations. In this paper, by combing these two types of crisp-fuzzy concept lattices and using interval-valued fuzzy sets, a novel crisp-fuzzy concept lattice is firstly presented, then the properties of the new model are discussed in detail. From two aspects of granular and algebraic structures, the new concept lattice is compared with two types of existing crisp-fuzzy concept lattices, which shows that the former has obvious advantages over the latter. Therefore, the work has not only enriched the theory of fuzzy concept lattice, but helpful for its application.