Fuzzy rough sets based on hybrid monotonic inclusion measures and similarity measures

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 IS
_λ
-fuzzy rough set based on a hybrid monotonic inclusion measure and a similarity measure. The properties of the IS
_λ
-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.