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    A Metaphor for Rough Set Theory: Modular Arithmetic

    Access Status
    Fulltext not available
    Authors
    Wolski, Marcin
    Gomolinska, A.
    Date
    2018
    Type
    Conference Paper
    
    Metadata
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    Citation
    Wolski, M. and Gomolinska, A. 2018. A Metaphor for Rough Set Theory: Modular Arithmetic, pp. 110-122.
    Source Title
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    DOI
    10.1007/978-3-319-99368-3_9
    ISBN
    9783319993676
    School
    School of Civil and Mechanical Engineering (CME)
    URI
    http://hdl.handle.net/20.500.11937/71542
    Collection
    • Curtin Research Publications
    Abstract

    © Springer Nature Switzerland AG 20118. Technically put, a metaphor is a conceptual mapping between two domains, which allows one to better understand the target domain; as Lakoff and Núñes put it, the main function of a metaphor is to allow us to reason about relatively abstract domains using the inferential structure of relatively concrete domains. In the paper we would like to apply this idea of framing one domain through conceptual settings of another domain to rough set theory (RST). The main goal is to construe rough sets in terms of the following mathematical metaphor: RST is a modular set-arithmetic. That is, we would like to map/project modular arithmetic onto rough sets, and, as a consequence, to redefine the fundamental concepts/objects of RST. Specifically, we introduce new topological operators (which play a similar role as remainders in modular arithmetic), discuss their formal properties, and finally apply them to the problem of vagueness (which has been intertwined with RST since the 1980’s).

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