Bags alias multisets have long been studied in computer science, but recently more attention is paid on bags. In this paper we consider generalized bags which include real-valued bags, fuzzy bags, and a region-valued bags. Basic definitions as well as their properties are established; advanced operations such as
-norms, and their duality are also studied. Moreover bag relations are discussed which has max-plus and max-min algebras as special cases. The reason why generalized bags are useful in applications is described. As two applications, bag-based data analysis and decision making based on convex function optimization related to bags are discussed.
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