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A Non-boolean Lattice Derived by Double Indiscernibility

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Transactions on Rough Sets XII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 6190))

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Abstract

The central notion of a rough set is the indiscernibility that is based on an equivalence relation. Because an equivalence relation shows strong bondage in an equivalence class, it forms a Galois connection and the difference between the upper and lower approximations is lost. Here, we introduce two different equivalence relations, one for the upper approximation and one for the lower approximation, and construct a composite approximation operator consisting of different equivalence relations. We show that a collection of fixed points with respect to the operator is a lattice and there exists a representation theorem for that construction.

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Authors and Affiliations

  1. Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Japan

    Yukio-Pegio Gunji & Taichi Haruna

Authors
  1. Yukio-Pegio Gunji
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  2. Taichi Haruna
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, R3T 5V6, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Insitute of Computing Science, Laboratory of Intelligent Decision Support Systems, Poznań University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    Roman Słowiński

  4. Department of Mathematics and Computing Science, Saint Mary’s University, B3H 3C3, Halifax, NS, Canada

    Pawan Lingras

  5. School of Electronics and Information Engineering, Tongji University, 201804, Shanghai, P.R. China

    Duoqian Miao

  6. Faculty of Medicine, Department of Medical Informatics, 89-1 Enya-cho, Shimane University, 693-8501, Izumo, Japan

    Shusaku Tsumoto

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Gunji, YP., Haruna, T. (2010). A Non-boolean Lattice Derived by Double Indiscernibility. In: Peters, J.F., Skowron, A., Słowiński, R., Lingras, P., Miao, D., Tsumoto, S. (eds) Transactions on Rough Sets XII. Lecture Notes in Computer Science, vol 6190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14467-7_11

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  • DOI: https://doi.org/10.1007/978-3-642-14467-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14466-0

  • Online ISBN: 978-3-642-14467-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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