Generalized multisets and rough approximations

A class of generalized multisets that includes real-valued multisets, fuzzy number-valued multisets, and fuzzy multisets is proposed. A generalized multiset has a membership of a closed region on a plane for each object. Upper and lower approximations of the generalized multisets are defined whereby rough approximations of real-valued multisets, fuzzy number-valued multisets, and fuzzy multisets are derived. Applications to fuzzy databases and information retrieval are suggested.