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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Generalized Bags, Bag Relations, and Applications to Data Analysis and Decision Making
verfasst von : Sadaaki Miyamoto
Erschienen in: Modeling Decisions for Artificial Intelligence
Verlag: Springer Berlin Heidelberg
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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
s
-norms,
t
-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.