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Bonds Between \(L\)-Fuzzy Contexts Over Different Structures of Truth-Degrees

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Book cover Formal Concept Analysis (ICFCA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9113))

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Abstract

We consider the problem of bonds between \(L\)-fuzzy contexts over different complete residuated lattices. For this purpose we define \((l,k)\)-connection and dual \((l,k)\)-connection – pairs of mappings between the residuated lattices based on Krupka’s results on factorizations of complete residuated lattices. We show that the bonds defined using the dual \((l,k)\)-connection have very natural properties.

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Notes

  1. 1.

    See [12] for motivations of the present research.

  2. 2.

    The notion of L-bond was introduced in [11]; however we adapt its definition the same way as in [8, 9].

  3. 3.

    In this section, we consistently denote dual \((l,k)\)-connections by prime, as \(\langle {\lambda ',\kappa '}\rangle \), to distinguish them from the non-dual \((l,k)\)-connections introduced in the previous section.

  4. 4.

    In this section \(\langle {\lambda ,\kappa }\rangle \) always denotes a dual \((l,k)\)-connection.

  5. 5.

    By \({\mathrm {proj}}_1\) and \({\mathrm {proj}}_2\) we denote projection of first and second entry of a pair, respectively; i.e. \({\mathrm {proj}}_1(\langle {a_1,a_2}\rangle ) \mapsto a_1, {\mathrm {proj}}_2(\langle {a_1,a_2}\rangle ) \mapsto a_2\).

References

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Acknowledgments

The author thanks to Ondrej Kridlo for valuable consultations.

Supported by grant No. 15-17899S, “Decompositions of Matrices with Boolean and Ordinal Data: Theory and Algorithms", of the Czech Science Foundation.

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Authors and Affiliations

  1. Data Analysis and Modeling Lab, Department of Computer Science, Palacky University, Olomouc 17. Listopadu 12, 77146, Olomouc, Czech Republic

    Jan Konecny

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  1. Jan Konecny
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Correspondence to Jan Konecny .

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Editors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    Jaume Baixeries

  2. Babeş-Bolyai University, Cluj-Napoca, Romania

    Christian Sacarea

  3. Departamento de Matemática Aplicada, Universidad de Málaga, Malaga, Spain

    Manuel Ojeda-Aciego

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Konecny, J. (2015). Bonds Between \(L\)-Fuzzy Contexts Over Different Structures of Truth-Degrees. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds) Formal Concept Analysis. ICFCA 2015. Lecture Notes in Computer Science(), vol 9113. Springer, Cham. https://doi.org/10.1007/978-3-319-19545-2_5

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  • DOI: https://doi.org/10.1007/978-3-319-19545-2_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19544-5

  • Online ISBN: 978-3-319-19545-2

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