Generalizations of multisets and rough approximations

Abstract

Three classes of generalizations of multisets are reviewed. They are real-valued multisets, fuzzy number–valued multisets, and fuzzy multisets. A family of generalized multisets that includes these three classes is proposed. A generalized multiset in this family 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.