Skip to main content
SpringerLink
Log in

Typicality of Features in Fuzzy Relational Compositions

  • Conference paper
  • First Online:
Fuzzy Techniques: Theory and Applications (IFSA/NAFIPS 2019 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1000))

Included in the following conference series:

  • 664 Accesses

Abstract

Fuzzy relations and their compositions have the same crucial importance for the fuzzy mathematics that is provided to mathematics by relations and their composition. The topic, since it attracted many scholars and influenced many areas in fuzzy modeling, has been extended on distinct directions including the recent one on the incorporation of excluding features. This article brings a mathematically similar yet semantically opposite extension, in particular, the concept of typical features. We show the appropriateness of such a new concept and investigate some of its properties. Furthermore, we discuss how the concept of typical features incorporated in fuzzy relational compositions may bring significant improvement of results of some applications. This fact is demonstrated on a real example of biological species classification.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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

Notes

  1. 1.

    The “S” in the name of the compositions implies the use of a t-conorm as this letter is often used to denote such an operation however, it has nothing common with our fuzzy relation S.

References

  1. Bandler, W., Kohout, L.: Fuzzy relational products and fuzzy implication operators. In: Proceedings of the International Workshop on Fuzzy Reasoning Theory and Applications, pp. 239–244. Queen Mary College, London (1978)

    Google Scholar 

  2. Bandler, W., Kohout, L.: Semantics of implication operators and fuzzy relational products. Int. J. Man-Mach. Stud. 12(1), 89–116 (1980)

    Article  MathSciNet  Google Scholar 

  3. Belohlavek, R.: Sup-t-norm and inf-residuum are one type of relational product: unifying framework and consequences. Fuzzy Sets Syst. 197, 45–58 (2012)

    Article  MathSciNet  Google Scholar 

  4. Běhounek, L., Daňková, M.: Relational compositions in fuzzy class theory. Fuzzy Sets Syst. 160(8), 1005–1036 (2009)

    Article  MathSciNet  Google Scholar 

  5. Bělohlávek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic; Plenum Press, Dordrecht; New York (2002)

    Book  Google Scholar 

  6. Cao, N., Holčapek, M., Štěpnička, M.: Extensions of fuzzy relational compositions based on generalized quantifiers. Fuzzy Sets Syst. 339, 73–98 (2018)

    Article  MathSciNet  Google Scholar 

  7. Cao, N., Štěpnička, M., Burda, M., Dolný, A.: Excluding features in fuzzy relational compositions. Expert Syst. Appl. 81, 1–11 (2017)

    Article  Google Scholar 

  8. Cao, N., Štěpnička, M., Burda, M., Dolný, A.: Fuzzy relational compositions based on grouping features. In: 9th International Conference on Knowledge and Systems Engineering (KSE), pp. 94–99 (2017)

    Google Scholar 

  9. Cao, N., Štěpnička, M., Burda, M., Dolný, A.: On the use of subproduct in fuzzy relational compositions based on grouping features. In: 2018 Information Processing and Management of Uncertainty in Knowledge-Based Systems, Applications. (Communications in Computer and Information Science), vol. 855, pp. 175–186 (2018)

    Google Scholar 

  10. Chung, F., Lee, T.: Analytical resolution and numerical identification of fuzzy relational systems. IEEE Trans. Syst. Man Cybern. 28, 919–924 (1998)

    Article  Google Scholar 

  11. De Baets, B.: Analytical solution methods for fuzzy relational equations. In: Dubois, D., Prade, H. (eds.) The Handbook of Fuzzy Set Series, vol. 1, pp. 291–340. Academic Kluwer Publishers, Boston (2000)

    Google Scholar 

  12. De Baets, B., Kerre, E.: Fuzzy relational compositions. Fuzzy Sets Syst. 60, 109–120 (1993)

    Article  MathSciNet  Google Scholar 

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

    Book  Google Scholar 

  14. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Boston (1999)

    Book  Google Scholar 

  15. Ožana, S., Burda, M., Hykel, M., Malina, M., Prášek, M., Bárta, D., Dolný, A.: Dragonfly hunter CZ: mobile application for biological species recognition in citizen science. PLoS ONE 14(1), e0210370 (2019)

    Article  Google Scholar 

  16. Pedrycz, W.: Fuzzy relational equations with generalized connectives and their applications. Fuzzy Sets Syst. 10, 185–201 (1983)

    Article  MathSciNet  Google Scholar 

  17. Štěpnička, M., Cao, N., Běhounek, L., Burda, M., Dolný, A.: Missing values and dragonfly operations in fuzzy relational compositions. Int. J. Approximate Reasoning (submitted)

    Google Scholar 

  18. Štěpnička, M., Holčapek, M.: Fuzzy relational compositions based on generalized quantifiers. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. PT II (IPMU 2014), Communications in Computer and Information Science, vol. 443, pp. 224–233. Springer, Berlin (2014)

    Chapter  Google Scholar 

Download references

Acknowledgements

Supported by LQ1602 NPU II “IT4Innovations in science” by the MŠMT.

Author information

Authors and Affiliations

  1. CE IT4I - IRAFM, University of Ostrava, 30. dubna 22, 701 03, Ostrava, Czech Republic

    Martin Štěpnička, Nhung Cao & Michal Burda

  2. Department of Biology and Ecology, Faculty of Sciences, University of Ostrava, Chittussiho 10, 710 00, Ostrava, Czech Republic

    Aleš Dolný

Authors
  1. Martin Štěpnička
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nhung Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michal Burda
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aleš Dolný
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Štěpnička .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA

    Ralph Baker Kearfott

  2. Center for Computing Research (CIC), Instituto Politecnico Nacional, Ciudad de Mexico, Mexico

    Ildar Batyrshin

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Marek Reformat

  4. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  5. Department of Computer Science, University of Texas at El Paso , El Paso, TX, USA

    Vladik Kreinovich

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Štěpnička, M., Cao, N., Burda, M., Dolný, A. (2019). Typicality of Features in Fuzzy Relational Compositions. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_56

Download citation

Publish with us

Policies and ethics

Search

Navigation