Skip to main content
SpringerLink
Log in

Betweenness Spaces: Morphism and Aggregation Functions

  • Conference paper
  • First Online:
Book cover Modeling Decisions for Artificial Intelligence (MDAI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11676))

  • 611 Accesses

Abstract

The notion of betweenness space or of a convex structure is an abstraction of the standard notion of convexity in a linear space. We first consider a ternary betweenness relation that gives rise to an interval space structure and then we propose a more general definition of betweenness. We study morphism between abstract convex spaces and we characterize aggregation function that are monotone with respect to a betweenness relation.

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. Cardin, M.: Aggregation over property-based preference domains. In: Torra, V., Mesiar, R., De Baets, B. (eds.) AGOP 2017. AISC, vol. 581, pp. 130–137. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-59306-7_13

    Chapter  Google Scholar 

  2. Cardin, M.: Sugeno integral on property-based preference domains. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT -2017. AISC, vol. 641, pp. 400–407. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66830-7_36

    Chapter  Google Scholar 

  3. Hedlíková, J.: Ternary spaces, media and Chebyshev sets. Czechoslovak Math. J. 33, 373–389 (1983)

    MathSciNet  MATH  Google Scholar 

  4. Nehring, K., Puppe, C.: The structure of strategy-proof social choice - part I: general characterization and possibility results on median spaces. J. Econ. Theory 135(1), 269–305 (2007)

    Article  MathSciNet  Google Scholar 

  5. Nehring, K., Puppe, C.: Abstract Arrowian aggregation. J. Econ. Theory 145, 467–494 (2010)

    Article  MathSciNet  Google Scholar 

  6. Rautenbach, D., Schäfer, P.M.: Strict betweennesses induced by posets as well as by graphs. Order 28, 89–97 (2011)

    Article  MathSciNet  Google Scholar 

  7. van de Vel, M.L.J.: Theory of Convex Structures North-Holland Mathematical Library, vol. 50. Elsevier, Amsterdam (1993)

    Google Scholar 

  8. Vannucci, S.: Weakly unimodal domains, anti-exchange properties, and coalitional strategy-proofness of aggregation rules. Math. Soc. Sci 84, 50–67 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Ca’ Foscari University of Venice, Sestiere Cannaregio 873, Venice, Italy

    Marta Cardin

Authors
  1. Marta Cardin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marta Cardin .

Editor information

Editors and Affiliations

  1. Maynooth University, Maynooth, Ireland

    Vicenç Torra

  2. Tamagawa University, Machida, Tokyo, Japan

    Yasuo Narukawa

  3. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  4. University of Milano-Bicocca, Milan, Italy

    Marco Viviani

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

Cardin, M. (2019). Betweenness Spaces: Morphism and Aggregation Functions. In: Torra, V., Narukawa, Y., Pasi, G., Viviani, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2019. Lecture Notes in Computer Science(), vol 11676. Springer, Cham. https://doi.org/10.1007/978-3-030-26773-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-26773-5_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26772-8

  • Online ISBN: 978-3-030-26773-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation