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Generalized Bags, Bag Relations, and Applications to Data Analysis and Decision Making

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Modeling Decisions for Artificial Intelligence (MDAI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5861))

Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Risk Engineering Faculty of Systems and Information Engineering, University of Tsukuba, Ibaraki, 305-8573, Japan

    Sadaaki Miyamoto

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  1. Sadaaki Miyamoto
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Editor information

Editors and Affiliations

  1. IIIA-CSIC, Campus UAB s/n, 08193, Bellaterra, Catalonia, Spain

    Vicenç Torra

  2. Toho Gakuen, 3-1-10 Naka, Kunitachi, 186-0004, Tokyo, Japan

    Yasuo Narukawa

  3. Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

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© 2009 Springer-Verlag Berlin Heidelberg

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Miyamoto, S. (2009). Generalized Bags, Bag Relations, and Applications to Data Analysis and Decision Making. In: Torra, V., Narukawa, Y., Inuiguchi, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2009. Lecture Notes in Computer Science(), vol 5861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04820-3_4

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  • DOI: https://doi.org/10.1007/978-3-642-04820-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04819-7

  • Online ISBN: 978-3-642-04820-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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