Skip to main content

Abstract

This paper continues previous work on additive generators of overlap functions, introducing the construction of grouping functions by means of additive generators, defined as a pair of one-place functions satisfying appropriate properties. Some important results are discussed.

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

Access this chapter

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bustince, H., Barrenechea, E., Pagola, M.: Image thresholding using restricted equivalence functions and maximizing the measures of similarity. Fuzzy Sets and Systems 158(5), 496–516 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Fodor, J., Roubens, M.: Fuzzy preference modelling and multicriteria decision support. Kluwer, New York (1994)

    Book  MATH  Google Scholar 

  3. Bustince, H., Pagola, M., Mesiar, R., Hüllermeier, E., Herrera, F.: Grouping, overlaps, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Transactions on Fuzzy Systems 20(3), 405–415 (2012)

    Article  Google Scholar 

  4. Bustince, H., Fernandez, J., Mesiar, R., Montero, J., Orduna, R.: Overlap functions. Nonlinear Analysis 72(3-4), 1488–1499 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Jurio, A., Bustince, H., Pagola, M., Pradera, A., Yager, R.: Some properties of overlap and grouping functions and their application to image thresholding. Fuzzy Sets and Systems 229, 69–90 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  6. Viceník, P.: Additive generators of associative functions. Fuzzy Sets and Systems 153(2), 137–160 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Mayor, G., Trillas, E.: On the representation of some aggregation functions. In: Proceedings of the XVI International Symposium on Multiple-Valued Logic (ISMVL 1986), Blacksburg, pp. 110–114 (1986)

    Google Scholar 

  8. Dimuro, G.P., Bedregal, B.C., Santiago, R.H.N., Reiser, R.H.S.: Interval additive generators of interval t-norms and interval t-conorms. Information Sciences 181(18), 3898–3916 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dimuro, G.P., Bedregal, B.R.C., Reiser, R.H.S., Santiago, R.H.N.: Interval additive generators of interval t-norms. In: Hodges, W., de Queiroz, R. (eds.) WoLLIC 2008. LNCS (LNAI), vol. 5110, pp. 123–135. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Bedregal, B.C., Dimuro, G.P., Santiago, R.H.N., Reiser, R.H.S.: On interval fuzzy S-implications. Information Sciences 180(8), 1373–1389 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dimuro, G.: On interval fuzzy numbers. In: 2011 Workshop-School on Theoretical Computer Science, WEIT 2011, pp. 3–8. IEEE, Los Alamitos (2011)

    Chapter  Google Scholar 

  12. Reiser, R.H.S., Dimuro, G.P., Bedregal, B.C., Santiago, R.H.N.: Interval valued QL-implications. In: Leivant, D., de Queiroz, R. (eds.) WoLLIC 2007. LNCS, vol. 4576, pp. 307–321. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Bedregal, B.C., Dimuro, G.P., Reiser, R.H.S.: An approach to interval-valued R-implications and automorphisms. In: Carvalho, J.P., Dubois, D., Kaymak, U., da Costa Sousa, J.M. (eds.) Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, IFSA/EUSFLAT, pp. 1–6 (2009)

    Google Scholar 

  14. Mesiarová-Zemánková, A.: Ranks of additive generators. Fuzzy Sets and Systems 160(14), 2032–2048 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  15. Dimuro, G.P., Bedregal, B.: Additive generators of overlap functions. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds.) Aggregation Functions in Theory and in Practise. AISC, vol. 228, pp. 167–178. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  16. Bedregal, B.C., Dimuro, G.P., Bustince, H., Barrenechea, E.: New results on overlap and grouping functions. Information Sciences 249, 148–170 (2013)

    Article  MathSciNet  Google Scholar 

  17. Rao, A.S., Georgeff, M.P.: Modeling rational agents within a BDI-architecture. In: Fikes, R., Sandewall, E. (eds.) Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning, pp. 473–484. Morgan Kaufmann, San Mateo (1991)

    Google Scholar 

  18. Dimuro, G.P., da Rocha Costa, A.C., Gonçalves, L.V., Hübner, A.: Centralized regulation of social exchanges between personality-based agents. In: Noriega, P., Vázquez-Salceda, J., Boella, G., Boissier, O., Dignum, V., Fornara, N., Matson, E. (eds.) COIN 2006. LNCS (LNAI), vol. 4386, pp. 338–355. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Dimuro, G.P., da Rocha Costa, A.C., Gonçalves, L.V., Pereira, D.: Recognizing and learning models of social exchange strategies for the regulation of social interactions in open agent societies. Journal of the Brazilian Computer Society 17, 143–161 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  20. Pereira, D.R., Gonçalves, L.V., Dimuro, G.P., da Rocha Costa, A.C.: Towards the self-regulation of personality-based social exchange processes in multiagent systems. In: Zaverucha, G., da Costa, A.L. (eds.) SBIA 2008. LNCS (LNAI), vol. 5249, pp. 113–123. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Dimuro, G.P., Bedregal, B., Bustince, H., Mesiar, R., Asiain, M.J. (2014). On Additive Generators of Grouping Functions. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-319-08852-5_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08852-5_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08851-8

  • Online ISBN: 978-3-319-08852-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics