Abstract: Interval-set provides a research tool for processing partially known concepts and for approximating undefinable or complex concepts. Concept lattices is a powerful tool for data analysis in machine learning, data mining, knowledge discovery, information retrieval, and so on. Interval-set concept lattices is the product of the combination concept lattices and the interval-set theory,which is a powerful tool for data analysis in machine learning, data mining, knowledge discovery and information retrieval on the information systems of partially known concepts or undefinable concepts. The attribute reduction of interval-set concept lattices is a kind of the method which reveals the elementary character of interval-set concept lattices attribute. This paper reveals the composition and structure of the attribute reduction of interval-set concept lattices. The equivalence relative necessary attributes are not in the same attribute reduction; and the intersection of attribute reduction and any relative necessary attribute equivalence class is nonempty. The set of the core attributes and the relative necessary attributes chosen by taking an attribute from each relative necessary attribute equivalence class must be an attribute reduction.

Key words: interval-set, interval-set concept lattices, attribute reduction