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On the Classification of Fuzzy-Attributes in Multi-adjoint Concept Lattices

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Advances in Computational Intelligence (IWANN 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7903))

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Abstract

In formal concept analysis, attribute reduction is an important preprocessing in order to obtain concept lattices, which provides fundamental information of the attributes, as well. This importance is increased in the fuzzy case.

This paper presents, in the general fuzzy framework of multi-adjoint concept lattices, a classification of the fuzzy-attributes of a context, which provides interesting properties of the attributes and its application to reduce the computational complexity for building this kind of concept lattices.

Partially supported by the Spanish Science Ministry projects TIN2009-14562-C05-03 and TIN2012-39353-C04-04, and by Junta de Andalucía project P09-FQM-5233.

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References

  1. Bělohlávek, R., Vychodil, V.: Reducing the size of fuzzy concept lattices by hedges. In: The 2005 IEEE International Conference on Fuzzy Systems, pp. 663–668 (2005)

    Google Scholar 

  2. Beydoun, G.: Formal concept analysis for an e-learning semantic web. Expert Systems with Applications 36(8), 10952–10961 (2009)

    Article  Google Scholar 

  3. Cornejo, M., Medina, J., Ramírez, E.: A comparative study of adjoint triples. Fuzzy Sets and Systems 211, 1–14 (2012)

    Article  Google Scholar 

  4. Formica, A.: Concept similarity in fuzzy formal concept analysis for semantic web. International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems 18(2), 153–167 (2010)

    Article  MathSciNet  Google Scholar 

  5. Formica, A.: Semantic web search based on rough sets and fuzzy formal concept analysis. Knowledge-Based Systems 26, 40–47 (2012)

    Article  Google Scholar 

  6. Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundation. Springer (1999)

    Google Scholar 

  7. Hájek, P.: Metamathematics of Fuzzy Logic. In: Trends in Logic. Kluwer Academic Publishers (1998)

    Google Scholar 

  8. Kang, X., Li, D., Wang, S., Qu, K.: Formal concept analysis based on fuzzy granularity base for different granulations. Fuzzy Sets and Systems 203, 33–48 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  9. Konecny, J.: Isotone fuzzy galois connections with hedges. Information Sciences 181(10), 1804–1817 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Konecny, J., Medina, J., Ojeda-Aciego, M.: Intensifying hedges and the size of multi-adjoint concept lattices with heterogeneous conjunctors. In: The 9th International Conference on Concept Lattices and Their Applications, pp. 245–256 (2012)

    Google Scholar 

  11. Kumar, C.A., Srinivas, S.: Concept lattice reduction using fuzzy k-means clustering. Expert Systems with Applications 37(3), 2696–2704 (2010)

    Article  Google Scholar 

  12. Li, L., Zhang, J.: Attribute reduction in fuzzy concept lattices based on the t-implication. Knowledge-Based Systems 23(6), 497–503 (2010)

    Article  Google Scholar 

  13. Medina, J.: Relating attribute reduction in formal, object-oriented and property-oriented concept lattices. Computers & Mathematics with Applications 64(6), 1992–2002 (2012)

    Article  MathSciNet  Google Scholar 

  14. Medina, J., Ojeda-Aciego, M.: Multi-adjoint t-concept lattices. Information Sciences 180(5), 712–725 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Medina, J., Ojeda-Aciego, M.: Towards attribute reduction in multi-adjoint concept lattices. In: The 7th International Conference on Concept Lattices and Their Applications, pp. 92–103 (2010)

    Google Scholar 

  16. Medina, J., Ojeda-Aciego, M., Ruiz-Calviño, J.: Formal concept analysis via multi-adjoint concept lattices. Fuzzy Sets and Systems 160(2), 130–144 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  18. Phan-Luong, V.: A framework for integrating information sources under lattice structure. Information Fusion 9, 278–292 (2008)

    Article  Google Scholar 

  19. Umbreit, S.: Formale Begriffsanalyse mit unscharfen Begriffen. PhD thesis, Halle, Saale (1995)

    Google Scholar 

  20. Wang, X., Zhang, W.: Relations of attribute reduction between object and property oriented concept lattices. Knowledge-Based Systems 21, 398–403 (2008)

    Article  Google Scholar 

  21. Wei, L., Qi, J.-J.: Relation between concept lattice reduction and rough set reduction. Knowledge-Based Systems 23(8), 934–938 (2010)

    Article  Google Scholar 

  22. Zhang, W., Wei, L., Qi, J.: Attribute reduction in concept lattice based on discernibility matrix. In: Ślęzak, D., Yao, J., Peters, J.F., Ziarko, W.P., Hu, X. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3642, pp. 157–165. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Dpt. de Estadística e I.O., University of Càdiz, Spain

    Maria Eugenia Cornejo & Eloisa Ramírez

  2. Dpt. de Matemáticas, University of Càdiz, Spain

    Jesús Medina-Moreno

Authors
  1. Maria Eugenia Cornejo
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  2. Jesús Medina-Moreno
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  3. Eloisa Ramírez
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Editor information

Editors and Affiliations

  1. Department of Computer Architecture and Computer Technology, University of Granada, Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Ignacio Rojas

  2. Department of Electronics Technology, University of Malaga, 29071, Malaga, Spain

    Gonzalo Joya

  3. Department of Electronics Engineering, Universitat Politecnica de Catalunya, 08034, Barcelona, Spain

    Joan Cabestany

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Cornejo, M.E., Medina-Moreno, J., Ramírez, E. (2013). On the Classification of Fuzzy-Attributes in Multi-adjoint Concept Lattices. In: Rojas, I., Joya, G., Cabestany, J. (eds) Advances in Computational Intelligence. IWANN 2013. Lecture Notes in Computer Science, vol 7903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38682-4_30

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  • DOI: https://doi.org/10.1007/978-3-642-38682-4_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38681-7

  • Online ISBN: 978-3-642-38682-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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