Skip to main content
SpringerLink
Log in

Andness-Directed Iterative OWA Aggregators

  • Conference paper
  • First Online:
Modeling Decisions for Artificial Intelligence (MDAI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12898))

Abstract

In this paper we introduce andness-directed iterative OWA aggregators. Iterative OWA aggregators belong to the family of OWA aggregators, where the aggregated value of additive aggregators is a scalar product of the sorted vector of arguments and the vector of logic weights that determine conjunctive or disjunctive properties of OWA aggregators. The overall logic properties of any OWA aggregator are characterized by andness (a conjunction degree) and orness (a disjunction degree), as well as the presence/absence of support for annihilators 0 and 1. In this paper we present iterative OWA aggregators where all logic weights are explicit functions (simple polynomials) of andness or orness. In such a way, the desired andness of aggregator is explicitly visible and easily adjustable, yielding ultimate simplicity in applications. Iterative OWA aggregators can also be weighted with importance weights.

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 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
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. Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. Syst. Man Cybernet. 18, 183–190 (1988)

    Google Scholar 

  2. Dujmović, J., Preferential neural networks. In: Antognetti, P., Milutinović, V. (eds.) Chapter 7 Neural Networks - Concepts, Applications, and Implementations, vol. II. Prentice-Hall Advanced Reference Series, pp. 155–206. Prentice-Hall, Englewood Cliffs (1991)

    Google Scholar 

  3. Dujmović, J.: Weighted conjunctive and disjunctive means and their application in system evaluation, Publikacije Elektrotehničkog Fakulteta, Serija Matematika i Fizika (Journal of the University of Belgrade School of EE, Series Mathematics and Physics) (483), 147–158 (1974). Available through JSTOR

    Google Scholar 

  4. Marichal, J.-L.: Aggregation operators for multicriteria decision aid. Ph.D. Dissertation, Institute of Mathematics, University of Liège, Liège, Belgium (1998)

    Google Scholar 

  5. Dujmović, J., Torra, V.: Properties and comparison of andness-characterized aggregators. Int. J. Intell. Syst. 36(3), 1366–1385 (2021)

    Article  Google Scholar 

  6. Torra, V.: Andness-directedness for operators of the OWA and WOWA families. Fuzzy Sets Syst. (2020, in press)

    Google Scholar 

  7. Dujmović, J.: Continuous preference logic for system evaluation. IEEE Trans. Fuzzy Syst. 15(6), 1082–1099 (2007)

    Article  Google Scholar 

  8. Troiano, L., Díaz, I.: An analytical solution to Dujmovic’s iterative OWA. In. J. Uncertain. Fuzziness Knowledge-Based Syst. 24(Suppl. 2), 165–179 (2016)

    Article  MathSciNet  Google Scholar 

  9. Ahn, B.S.: An alternative approach to obtaining an analytical solution to Dujmovic’s iterative OWA. Internat. J. Uncertain. Fuzziness Knowledge-Based Syst. 26(2), 261–267 (2018)

    Article  MathSciNet  Google Scholar 

  10. Dujmović, J., Nine forms of andness/orness. In: Kovalerchuk, B. (ed.) Proceedings of the Second IASTED International Conference on Computational Intelligence, pp. 276–281 (2006). ISBN:Hardcopy:0–88986-602-3/CD: 0-88986-603-1

    Google Scholar 

  11. Dujmović, J., Soft Computing Evaluation Logic. John Wiley & Sons, Hoboken (2018)

    Google Scholar 

  12. Miller, G.A.: The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol. Rev. 63, 81–97 (1956)

    Article  Google Scholar 

  13. Dujmović, J.: Weighted compensative logic with adjustable threshold andness and orness. IEEE Transa. Fuzzy Syst. 23(2), 270–290 (2015). https://doi.org/10.1109/TFUZZ.2014.2312018

  14. Dujmović, J.: Graded logic for decision support systems. Int. J. Intell. Syst. 34, 2900–2919 (2019). https://doi.org/10.1002/int.22177

    Article  Google Scholar 

  15. Beliakov, G., Dujmović, J.: Extension of bivariate means to weighted means of several arguments by using binary trees. Inf. Sci. 331, 137–147 (2016). https://doi.org/10.1016/j.ins.2015.10.040

    Article  MathSciNet  MATH  Google Scholar 

  16. Dujmović, J., Beliakov, G.: Idempotent weighted aggregation based on binary aggregation trees. Int. J. Intell. Syst. 32(1), 31–50 (2017). https://doi.org/10.1002/int.21828

    Article  Google Scholar 

  17. Troiano, L., Yager, R.R.: Recursive and Iterative OWA operators. Internat. J. Uncertain. Fuzziness Knowledge-Based Syst. 13(6), 579–599 (2005)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA, 94132, USA

    Jozo Dujmović

Authors
  1. Jozo Dujmović
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jozo Dujmović .

Editor information

Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Vicenç Torra

  2. Tamagawa University, Tokyo, Japan

    Yasuo Narukawa

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dujmović, J. (2021). Andness-Directed Iterative OWA Aggregators. In: Torra, V., Narukawa, Y. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2021. Lecture Notes in Computer Science(), vol 12898. Springer, Cham. https://doi.org/10.1007/978-3-030-85529-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-85529-1_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85528-4

  • Online ISBN: 978-3-030-85529-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation