Skip to main content
SpringerLink
Log in

On the Problem of Comparing Ordered Ordinary Fuzzy Multisets

  • Conference paper
  • First Online:
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 854))

  • 1062 Accesses

Abstract

In this work we deal with a particular type of hesitant fuzzy set, in the case where membership values can appear multiple times and are ordered. They are called ordered ordinary fuzzy multisets. Some operations between them are introduced by means of an extension principle. In particular, the divergence measures between two of these multisets are defined and we have studied in detail the local family of divergences. Finally, these measures are related to the ones given for ordinary fuzzy sets.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Anthony, M., Hammer, P.L.: A Boolean measure of similarity. Discrete Appl. Math. 154(16), 2242–2246 (2006)

    Article  MathSciNet  Google Scholar 

  2. Bouchon-Meunier, B., Rifqi, M., Bothorel, S.: Towards general measures of comparison of objects. Fuzzy Sets Syst. 84, 143–153 (1996)

    Article  MathSciNet  Google Scholar 

  3. Beliakov, G., Bustince, H., Calvo, T.: A Practical Guide to Averaging Functions. Studies in Fuzziness and Soft Computing, vol. 329. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-319-24753-3. ISBN 978-3-319-24751-9

    Book  Google Scholar 

  4. Couso, I., Garrido, L., Sánchez, L.: Similarity and dissimilarity measures between fuzzy sets: a formal relational study. Inf. Sci. 229, 122–141 (2013)

    Article  MathSciNet  Google Scholar 

  5. Dubois, D., Prade, H.: Fundamentals of Fuzzy Sets. Kluwer Academic Publishers, Massachusetts (2000)

    Book  Google Scholar 

  6. Grattan-Guinness, I.: Fuzzy membership mapped onto intervals and many-valued quantities. Math. Logic Q. 22–1, 149–160 (1976)

    Article  MathSciNet  Google Scholar 

  7. Klement, P., Mesiar, R., Pap, E.: Triangular Norms. Trends in Logic, vol. 8. Springer, Heidelberg (2000). https://doi.org/10.1007/978-94-015-9540-7

    Book  Google Scholar 

  8. Klir, G.J., Folger, T.A.: Fuzzy Sets Uncertainty and Information. Prentice-Hall, Englewood Cliffs (1988)

    MATH  Google Scholar 

  9. Kobza, V., Janiš, V., Montes, S.: Generalizated local divergence measures. J. Intell. Fuzzy Syst. 33, 337–350 (2017)

    Article  Google Scholar 

  10. Li, Y., Qin, K., He, X.: Some new approaches to constructing similarity measures. Fuzzy Sets Syst. 234(1), 46–60 (2014)

    Article  MathSciNet  Google Scholar 

  11. Lui, X.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets Syst. 52, 305–318 (1992)

    Article  MathSciNet  Google Scholar 

  12. Montes, I., Pal, N.R., Janiš, V., Montes, S.: Divergence measures for intuitionistic fuzzy sets. IEEE Trans. Fuzzy Syst. 23(2), 444–456 (2015)

    Article  Google Scholar 

  13. Montes, I., Janiš, V., Pal, N.R., Montes, S.: Local divergences for Atanassov intuitionistic fuzzy sets. IEEE Trans. Fuzzy Syst. (in press). https://doi.org/10.1109/TFUZZ.2015.2457447

  14. Montes, S., Couso, I., Gil, P., Bertoluzza, C.: Divergence measure between fuzzy sets. Int. J. Approx. Reason. 30, 91–105 (2002)

    Article  MathSciNet  Google Scholar 

  15. Rodríguez, R.M., Bedregal, B., Bustince, H., Dong, Y.C., Farhadinia, B., Kahraman, C., Martínez, L., Torra, V., Xu, Y.J., Xu, Z.S., Herrera, F.: A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf. Fusion 29, 89–97 (2016)

    Article  Google Scholar 

  16. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25–6, 529–539 (2010)

    MATH  Google Scholar 

  17. Valverde, L., Ovchinnikov, S.: Representations of T-similarity relations. Fuzzy Sets Syst. 159(17), 2211–2220 (2008)

    Article  MathSciNet  Google Scholar 

  18. Wilbik, A., Keller, J.M.: A fuzzy measure similarity between sets of linguistic summaries. IEEE Trans. Fuzzy Syst. 21(1), 183–189 (2013)

    Article  Google Scholar 

  19. Xu, Z.S.: Hesitant Fuzzy Sets Theory. Studies in Fuzziness and Soft Computing, vol. 314. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-319-04711-9

    Book  Google Scholar 

  20. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

  21. Zadeh, L.A.: A note on similarity-based definitions of possibility and probability. Inf. Sci. 267, 334–336 (2014)

    Article  MathSciNet  Google Scholar 

  22. Zhang, C., Fu, H.: Similarity measures on three kinds of fuzzy sets. Pattern Recogn. Lett. 27(12), 1307–1317 (2006)

    Article  Google Scholar 

Download references

Acknowledgment

Authors acknowledge financial support by the Spanish Ministry under Projects TIN2014-59543-P and TIN2017-87600-P.

Author information

Authors and Affiliations

  1. UNIMODE Research Unit, University of Oviedo, Oviedo, Spain

    Ángel Riesgo, Pedro Alonso, Irene Díaz & Susana Montes

  2. Matej Bel University, Banská Bystrica, Slovakia

    Vladimír Janiš & Vladimír Kobza

Authors
  1. Ángel Riesgo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pedro Alonso
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Irene Díaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vladimír Janiš
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Vladimír Kobza
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Susana Montes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Susana Montes .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Riesgo, Á., Alonso, P., Díaz, I., Janiš, V., Kobza, V., Montes, S. (2018). On the Problem of Comparing Ordered Ordinary Fuzzy Multisets. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 854. Springer, Cham. https://doi.org/10.1007/978-3-319-91476-3_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91476-3_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91475-6

  • Online ISBN: 978-3-319-91476-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation