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Attribute Reduction in Rough Set Theory and Formal Concept Analysis

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Rough Sets (IJCRS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10314))

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Abstract

Rough Set Theory (RST) and Formal Concept Analysis (FCA) are two mathematical tools for data analysis which, in spite of considering different philosophies, are closely related. In this paper, we study the relation between the attribute reduction mechanisms in FCA and in RST. Different properties will be introduced which provide a new size reduction mechanism in FCA based on the philosophy of RST.

Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (FEDER) project TIN2016-76653-P.

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Notes

  1. 1.

    We assume that the reader is familiar with the notions related to classical theory of propositional logic [8, 12].

  2. 2.

    Originally these operators were denoted as \('\) by Ganter and Wille and they were called derivation operators. In order to differentiate between the mapping on the set of objects and on the set of attributes, we have changed the notation.

  3. 3.

    Note that the discernibility matrix is symmetric due to the discernibility relation is reflexive.

  4. 4.

    In order to simplify the notation, we will write \((^{\uparrow _1},^{\downarrow ^1})\) and \((^{\uparrow _2},^{\downarrow ^2})\), instead of \((^{\uparrow _{D_1}},^{\downarrow ^{D_1}})\) and \((^{\uparrow _{D_2}},^{\downarrow ^{D_2}})\) to denote the concept-forming operators in the reduced contexts by \(D_1\) and \(D_2\), respectively.

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Authors and Affiliations

  1. Departament of Mathematics, Universidad de Cádiz, Cádiz, Spain

    María José Benítez-Caballero, Jesús Medina & Eloísa Ramírez-Poussa

Authors
  1. María José Benítez-Caballero
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  2. Jesús Medina
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  3. Eloísa Ramírez-Poussa
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Corresponding author

Correspondence to Eloísa Ramírez-Poussa .

Editor information

Editors and Affiliations

  1. Polish-Japanese Academy of Information Technology, Warsaw, Poland

    Lech Polkowski

  2. University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

  3. University of Warmia and Mazury, Olsztyn, Poland

    Piotr Artiemjew

  4. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

  5. Southwest Jiaotong University, Chengdu, China

    Dun Liu

  6. Warsaw University, Warszawa, Poland

    Dominik Ślęzak

  7. Silesian University, Sosnowiec, Poland

    Beata Zielosko

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Benítez-Caballero, M.J., Medina, J., Ramírez-Poussa, E. (2017). Attribute Reduction in Rough Set Theory and Formal Concept Analysis. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10314. Springer, Cham. https://doi.org/10.1007/978-3-319-60840-2_37

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  • DOI: https://doi.org/10.1007/978-3-319-60840-2_37

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