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A Metaphor for Rough Set Theory: Modular Arithmetic

  • Marcin Wolski
  • Anna Gomolińska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11103)

Abstract

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).

Keywords

Rough set Modular arithmetic Remainder Topolgy Boundary Vagueness 

Notes

Acknowledgements

We are greatly indebted to anonymous referees for their valuable comments and corrections.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Logic and Cognitive ScienceMaria Curie-Skłodowska UniversityLublinPoland
  2. 2.Faculty of Mathematics and InformaticsUniversity of BiałystokBiałystokPoland

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