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Concept Granular Computing Based on Lattice Theoretic Setting

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Book cover Human-Centric Information Processing Through Granular Modelling

Part of the book series: Studies in Computational Intelligence ((SCI,volume 182))

Abstract

Based on the theory of concept lattice and fuzzy concept lattice, a mathematical model of a concept granular computing system is established, and relationships of the system and concept lattices, various variable threshold concept lattices and fuzzy concept lattices are then investigated. For this system, concept granules, sufficiency information granules and necessity information granules which are used to express different relations between a set of objects and a set of attributes are proposed. Approaches to construct sufficiency and necessity information granules are also shown. Some iterative algorithms to form concept granules are proposed. It is proved that the concept granules obtained by the iterative algorithms are the sub-concept granules or sup-concept granules under some conditions for this system. Finally, we give rough approximations based on fuzzy concept lattice in formal concept analysis.

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Author information

Authors and Affiliations

  1. Faculty of Science, Xi’an Jiaotong University, Shaanxi, 710049, P.R.China

    Wen-xiu Zhang & Hong-zhi Yang

  2. Department of Mathematics and Information Science, Faculty of Science, Chang’an University, Shaanxi, 710064, P.R.China

    Jian-min Ma

  3. School of Management, Xi’an University of Architecture & Technology, Shaanxi, 710055, P.R.China

    Guo-fang Qiu

Authors
  1. Wen-xiu Zhang
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  2. Hong-zhi Yang
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  3. Jian-min Ma
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  4. Guo-fang Qiu
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Editor information

Editors and Affiliations

  1. School of Computer Science, The University of Nottingham, Malaysia Campus, Jalan Broga, 43500, Semenyih Selangor Darul Ehsan, Malaysia

    Andrzej Bargiela

  2. Department of Electrical & Computer Engineering, University of Alberta, AB T6R 2G7, Edmonton, Canada

    Witold Pedrycz

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Zhang, Wx., Yang, Hz., Ma, Jm., Qiu, Gf. (2009). Concept Granular Computing Based on Lattice Theoretic Setting. In: Bargiela, A., Pedrycz, W. (eds) Human-Centric Information Processing Through Granular Modelling. Studies in Computational Intelligence, vol 182. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92916-1_4

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  • DOI: https://doi.org/10.1007/978-3-540-92916-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92915-4

  • Online ISBN: 978-3-540-92916-1

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