Skip to main content
SpringerLink
Log in

Concept Lattices as a Reduction Tool for Fuzzy Relation Equations

  • Conference paper
  • First Online:
Graph-Based Representation and Reasoning (ICCS 2023)

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

Included in the following conference series:

  • 170 Accesses

Abstract

Recently, a procedure to reduce multi-adjoint relation equations has been published. Such method relies on the strong existing link between fuzzy relation equations and concept lattices, and more specifically, it is based on attribute reduction techniques. In this paper, we illustrate the reduction mechanism for the specific case of fuzzy relation equations on a more general structure than a residuated lattice, in which an adjoint triple is considered instead of a left continuous t-norm and its residuated implication.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Digital forensics: Evidence analysis via intelligent systems and practices DigForASP - Action COST CA17124. https://digforasp.uca.es

  2. Antoni, L., Cornejo, M.E., Medina, J., Ramirez, E.: Attribute classification and reduct computation in multi-adjoint concept lattices. IEEE Trans. Fuzzy Syst. 29, 1121–1132 (2020)

    Google Scholar 

  3. Cornejo, M.E., Medina, J., Ramírez-Poussa, E.: Algebraic structure and characterization of adjoint triples. Fuzzy Sets Syst. 425, 117–139 (2021)

    Article  MathSciNet  Google Scholar 

  4. De Baets, B.: Sup-T equations: state of the art. In: Kaynak, O., Zadeh, L.A., Türkşen, B., Rudas, I.J. (eds.) Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications. NATO ASI Series, vol. 162, pp. 80–93. Springer, Heidelberg (1998). https://doi.org/10.1007/978-3-642-58930-0_5

  5. Di Martino, F., Sessa, S.: A novel image similarity measure based on greatest and smallest eigen fuzzy sets. Symmetry 15(5), 1104 (2023)

    Article  Google Scholar 

  6. Di Nola, A., Sanchez, E., Pedrycz, W., Sessa, S.: Fuzzy Relation Equations and Their Applications to Knowledge Engineering. Kluwer Academic Publishers, Norwell (1989)

    Book  MATH  Google Scholar 

  7. Díaz, J.C., Medina, J.: Multi-adjoint relation equations: definition, properties and solutions using concept lattices. Inf. Sci. 253, 100–109 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lobo, D., López-Marchante, V., Medina, J.: On the impact of sup-compositions in the resolution of multi-adjoint relation equations. Math. Methods Appl. Sci., 1–18 (2023, in press). https://doi.org/10.1002/mma.9414

  9. Lobo, D., López-Marchante, V., Medina, J.: Reducing fuzzy relation equations via concept lattices. Fuzzy Sets Syst. 463, 108465 (2023)

    Article  MathSciNet  Google Scholar 

  10. Medina, J.: Multi-adjoint property-oriented and object-oriented concept lattices. Inf. Sci. 190, 95–106 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Peeva, K., Kyosev, Y.: Fuzzy Relational Calculus: Theory, Applications and Software. World Scientific Publishing Company (2004)

    Google Scholar 

  12. Rubio-Manzano, C., Alfonso-Robaina, D., Díaz-Moreno, J.C., Malleuve-Martínez, A., Medina, J.: Determining cause-effect relations from fuzzy relation equations. Commun. Comput. Inf. Sci. 1601, 155–166 (2022)

    Google Scholar 

  13. Tiwari, V.L., Thapar, A., Bansal, R.: A genetic algorithm for solving nonlinear optimization problem with max-archimedean bipolar fuzzy relation equations. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 31(02), 303–326 (2023)

    Article  MathSciNet  Google Scholar 

  14. Xiao, G., Hayat, K., Yang, X.: Evaluation and its derived classification in a server-to-client architecture based on the fuzzy relation inequality. Fuzzy Optim. Decis. Making 22, 213–245 (2023)

    Article  MATH  Google Scholar 

  15. Yang, X.P.: Random-term-absent addition-min fuzzy relation inequalities and their lexicographic minimum solutions. Fuzzy Sets Syst. 440, 42–61 (2022)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Partially supported by the 2014–2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in projects PID2019-108991GB-I00 and PID2022-137620NB-I00, with the Ecological and Digital Transition Projects 2021 of the Ministry of Science and Innovation in project TED2021-129748B-I00, and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and by the European Cooperation in Science & Technology (COST) Action CA17124.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Cádiz, Cádiz, Spain

    David Lobo, Víctor López-Marchante & Jesús Medina

Authors
  1. David Lobo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Víctor López-Marchante
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jesús Medina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Lobo .

Editor information

Editors and Affiliations

  1. Universidad de Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  2. FernUniversität in Hagen, Hagen, Germany

    Kai Sauerwald

  3. Humboldt-Universität zu Berlin, Berlin, Germany

    Robert Jäschke

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Lobo, D., López-Marchante, V., Medina, J. (2023). Concept Lattices as a Reduction Tool for Fuzzy Relation Equations. In: Ojeda-Aciego, M., Sauerwald, K., Jäschke, R. (eds) Graph-Based Representation and Reasoning. ICCS 2023. Lecture Notes in Computer Science(). Springer, Cham. https://doi.org/10.1007/978-3-031-40960-8_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-40960-8_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-40959-2

  • Online ISBN: 978-3-031-40960-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation