Rough set theory and fuzzy set theory hold the topic of dealing with imperfect knowledge. Recent literature have shown both theories can be combined into a more expressive framework for modeling and processing incomplete information systems. According to the hierarchical characteristic of fuzzy sets, this paper presents the definitions of λ-weak fuzzy approximation space and ISλ-fuzzy rough set based on a hybrid monotonic inclusion measure and a similarity measure. The properties of the ISλ-fuzzy rough set are investigated. The approximate operators of a fuzzy decision concept and the relative decision rules will be derived from the fuzzy rough approximate operators.