Skip to main content
SpringerLink
Log in
Book cover

Fuzzy Logic and Information Fusion pp 101–121Cite as

New Advances in the Aggregation of Asymmetric Distances. The Bounded Case

  • Chapter
  • First Online:

  • 681 Accesses

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 339))

Abstract

In 1981, J. Borsík and J. Doboš studied the problem of how to merge, by means of a function, a family of distances into a single one. To this end, they introduced the notion of distance aggregation function and gave a characterization of such functions. Later on, in 2010, the notion of distance aggregation function was extended to the framework of asymmetric distances by G. Mayor and O. Valero. Thus, asymmetric distance aggregation functions were introduced and a characterization of this new type of functions was also given. Concretely, the aforesaid characterization states that the functions which allow to merge a family of asymmetric distances into a single one are exactly those that are amenable, monotone and subadditive. In the present chapter we consider the problem of aggregating a family of bounded asymmetric distances. To this end, the notion of bounded asymmetric distance aggregation function is introduced and a full description of such functions is provided. The obtained results are illustrated by means of examples. Furthermore, the relationship between asymmetric aggregation functions and the bounded ones is discussed.

This is a preview of subscription content, 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   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

References

  1. G. Beliakov, H. Bustince, T. Calvo, A Practical Guide to Averaging Functions. Studies of Fuzziness and Soft Computing, vol. 329 (Springer, Heilderberg, 2015)

    Google Scholar 

  2. G. Beliakov, A. Pradera, T. Calvo, Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness and Soft Computing, vol. 221 (2007)

    Google Scholar 

  3. J. Bolton, P. Gader, J.N. Wilson, Discrete Choquet integral as a distance metric. IEEE T. Fuzzy Syst. 16, 1107–1110 (2008)

    Google Scholar 

  4. J. Borsik, J. Doboš, On a product of metric spaces. Math. Slovaca 31, 193–205 (1981)

    MathSciNet  MATH  Google Scholar 

  5. J. Casasnovas, F. Roselló, Averaging fuzzy biopolymers. Fuzzy Set. Syst. 152, 139–158 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. E. Castiñeira, A. Pradera, E. Trillas, On distances aggregation, in Proceedings of the Information Processing and Management of Uncertainty in Knowledge-based Systems International Conference (2000), pp. 693–700

    Google Scholar 

  7. E. Castiñeira, A. Pradera, E. Trillas, On the aggregation of some classes of fuzzy relations, in Technologies for Constructing Intelligent Systems, ed. by B. Bouchon-Meunier, J. Gutierrez, L. Magdalena, R. Yager (Springer, 2002), pp. 125–147

    Google Scholar 

  8. E.T. Copson, Metric Spaces (Cambridge University Press, Cambridge, 1968)

    Book  MATH  Google Scholar 

  9. J. Doboš, Metric Preserving Functions (Štroffek, Košice, 1998)

    MATH  Google Scholar 

  10. L.M. García-Raffi, S. Romaguera, M.P. Schellekens, Applications of the complexity space to the general probabilistic divide and conquer algorithms. J. Math. Anal. Appl. 348, 346–355 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Grabisch, J.L. Marichal, R. Mesiar, E. Pap, Aggregation Functions (Cambridge University Press, New York, 2009)

    Book  MATH  Google Scholar 

  12. P. Hitzler, A.K. Seda, Mathematical Aspects of Logic Programming Semantics (CRC Press, Boca Raton, 2010)

    Book  MATH  Google Scholar 

  13. E.P. Klement, R. Mesiar, E. Pap, Triangular Norms (Kluwer Academic Publishers, Dordrecht, 2000)

    Book  MATH  Google Scholar 

  14. H.P.A. Künzi, Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology, in Handbook of the History of General Topology, vol. 3, ed. by C.E. Aull, R. Lowen (Kluwer Academic Publishers, 2001), pp. 853–968

    Google Scholar 

  15. J. Martín, G. Mayor, O. Valero, On quasi-metric aggregation functions and fixed point theorems. Fuzzy Set. Syst. 228, 188–104 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. G. Mayor, O. Valero, Aggregating asymmetric distances in computer sciences,in Computational Intelligence in Decision and Control, vol. I, ed. by D. Ruan et al. (World Scientific, 2008), pp. 477–482

    Google Scholar 

  17. G. Mayor, O. Valero, Aggregation of asymmetric distances in computer science. Inf. Sci. 180, 803–812 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. S.G. Matthews, Partial metric topology. Ann. New York Acad. Sci. 728, 183–197 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  19. E.A. Ok, Real Analysis with Economic Applications (Princeton University Press, New Jersey, 2007)

    MATH  Google Scholar 

  20. V. Pestov, A. Stojmirović, Indexing schemes for similarity search: an illustrated paradigm. Fund. Inf. 70, 367–385 (2006)

    MathSciNet  MATH  Google Scholar 

  21. V. Pestov, A. Stojmirović, Indexing schemes for similarity search in datasets of short protein fragments. Inf. Syst. 32, 1145–1165 (2007)

    Article  Google Scholar 

  22. I. Pokorný, Some remarks on metric preserving functions of several variables. Tatra Mt. Math. Publ. 8, 89–92 (1996)

    MathSciNet  MATH  Google Scholar 

  23. A. Pradera, E. Trillas, A note on pseudometrics aggregation. Int. J. Gen. Syst. 31, 41–51 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. S. Romaguera, E.A. Sánchez-Pérez, O. Valero, Computing complexity distances between algorithms. Kybernetika 39, 569–582 (2003)

    MathSciNet  MATH  Google Scholar 

  25. S. Romaguera, P. Tirado, O. Valero, New results on mathematical foundations of asymptotic complexity analysis of algorithms via complexity space. Int. J. Comput. Math. 89, 1728–1741 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. S. Romaguera, M. Schellekens, O. Valero, The complexity space of partial functions: a connection between complexity analysis and denotational semantics. Int. J. Comput. Math. 88, 1819–1829 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Romaguera, O. Valero, Asymptotic complexity analysis and denotational semantics for recursive programs based on complexity spaces, in Semantics-Advances in Theories and Mathematical Models, vol. 1, ed. by M. Afzal (InTech Open Science, 2012), pp. 99–120

    Google Scholar 

  28. S. Romaguera, O. Valero, E.A. Sánchez-Pérez, Quasi-normed monoids and quasi-metrics, Publ. Math.-Debrecen 62, 53–69 (2003)

    Google Scholar 

  29. S. Saminger, R. Mesiar, U. Bodenhofer, Domination of aggregation operators and preservation of transitivity. Int. J. Uncertain. Fuzz. 10, 11–35 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  30. M. Schellekens, The Smyth completion: a common foundation for denotational semantics and complexity analysis. Electron. Notes Theor. Comput. Sci. 1, 211–232 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to express their gratitude for all the affection and the strong support received from Professor Gaspar Mayor over the years and for all his work as a mentor throughout his career. The authors acknowledge the support of the Spanish Ministry of Economy and Competitiveness, under grants TIN2012-32482, TIN2013-42795-P and TIN2014-56381-REDT (LODISCO).

Author information

Authors and Affiliations

  1. Universitat de les Illes Balears, Palma de Mallorca, Illes Balears, Spain

    Isabel Aguiló, Pilar Fuster-Parra, Javier Martín, Jaume Suñer & Oscar Valero

  2. Universidad de Alcalá, Alcalá de Henares, Madrid, Spain

    Tomasa Calvo Sánchez

Authors
  1. Isabel Aguiló
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomasa Calvo Sánchez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pilar Fuster-Parra
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Javier Martín
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jaume Suñer
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Oscar Valero
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oscar Valero .

Editor information

Editors and Affiliations

  1. University of Alcalá, Alcalá de Henares, Spain

    Tomasa Calvo Sánchez

  2. University of Balearic Islands, Palma, Spain

    Joan Torrens Sastre

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Aguiló, I., Calvo Sánchez, T., Fuster-Parra, P., Martín, J., Suñer, J., Valero, O. (2016). New Advances in the Aggregation of Asymmetric Distances. The Bounded Case. In: Calvo Sánchez, T., Torrens Sastre, J. (eds) Fuzzy Logic and Information Fusion. Studies in Fuzziness and Soft Computing, vol 339. Springer, Cham. https://doi.org/10.1007/978-3-319-30421-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30421-2_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30419-9

  • Online ISBN: 978-3-319-30421-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation