Skip to main content
SpringerLink
Log in

New Types of Decomposition Integrals and Computational Algorithms

  • Conference paper
  • First Online:
Information Technology, Systems Research, and Computational Physics (ITSRCP 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 945))

  • 316 Accesses

Abstract

In this paper we define two new types of decomposition integrals, namely the chain and the min-max integral and prove some of their properties. Their superdecomposition duals are also mentioned. Based on the wide applicability of decomposition integrals, some computational algorithms and their complexity are discussed.

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 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Choquet, G.: Theory of capacities. Annales de l’Institut Fourier 5, 131–295 (1954). https://doi.org/10.5802/aif.53

    Article  MathSciNet  MATH  Google Scholar 

  2. Even, Y., Lehrer, E.: Decomposition-integral: unifying Choquet and the concave integrals. Econ. Theory 56, 33–58 (2014). https://doi.org/10.1007/s00199-013-0780-0

    Article  MathSciNet  MATH  Google Scholar 

  3. Lehrer, E.: A new integral for capacities. Econ. Theory 39, 157–176 (2009). https://doi.org/10.1007/s00199-007-0302-z

    Article  MathSciNet  MATH  Google Scholar 

  4. Mesiar, R., Li, J., Pap, E.: Superdecomposition integrals. Fuzzy Sets Syst. 259, 3–11 (2015). https://doi.org/10.1016/j.fss.2014.05.003

    Article  MathSciNet  MATH  Google Scholar 

  5. Mesiar, R., Stupňanová, A.: Decomposition integrals. Int. J. Approx. Reason. 54, 1252–1259 (2013). https://doi.org/10.1016/j.ijar.2013.02.001

    Article  MathSciNet  MATH  Google Scholar 

  6. Šeliga, A.: A note on the computational complexity of Lehrer integral. In: Advances in Architectural, Civil and Environmental Engineering: 27th Annual PhD Student Conference on Applied Mathematics, Applied Mechanics, Geodesy and Cartography, Landscaping, Building Technology, Theory and Structures of Buildings, Theory and Structures of Civil Engineering Works, Theory and Environmental Technology of Buildings, Water Resources Engineering, pp. 62–65 (2017). ISBN 978-80-227-4751-6

    Google Scholar 

  7. Šeliga, A.: New types of decomposition integrals and computational algorithms. In: Kulczycki, P., Kowalski, P.A., Łukasik, S. (eds.) Contemporary Computational Science, p. 93. AGH-UST Press, Cracow (2018)

    Google Scholar 

  8. Shilkret, N.: Maxitive measure and integration. Indagationes Mathematicae 33, 109–116 (1971). https://doi.org/10.1016/S1385-7258(71)80017-3

    Article  MathSciNet  MATH  Google Scholar 

  9. Sugeno, M.: Theory of fuzzy integrals and its applications. Doctoral thesis, Tokyo Institute of Technology (1974)

    Google Scholar 

  10. Yang, Q.: The Pan-integral on the fuzzy measure space. Fuzzy Math. 3, 107–114 (1985)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgement

This work was supported by the grants APVV-14-0013 and VEGA 1/0682/16.

Author information

Authors and Affiliations

  1. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05, Bratislava, Slovakia

    Adam Šeliga

Authors
  1. Adam Šeliga
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adam Šeliga .

Editor information

Editors and Affiliations

  1. Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Krakow, Poland

    Piotr Kulczycki

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  3. Faculty of Engineering Sciences, Széchenyi István University, Győr, Hungary

    László T. Kóczy

  4. Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  5. Department of Electronic Systems, Aalborg University, Aalborg, Denmark

    Rafal Wisniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Šeliga, A. (2020). New Types of Decomposition Integrals and Computational Algorithms. In: Kulczycki, P., Kacprzyk, J., Kóczy, L., Mesiar, R., Wisniewski, R. (eds) Information Technology, Systems Research, and Computational Physics. ITSRCP 2018. Advances in Intelligent Systems and Computing, vol 945. Springer, Cham. https://doi.org/10.1007/978-3-030-18058-4_29

Download citation

Publish with us

Policies and ethics

Search

Navigation