IDEAS home Printed from https://ideas.repec.org/a/spr/fuzinf/v4y2012i4d10.1007_s12543-012-0124-y.html
   My bibliography  Save this article

Approximation of fuzzy integrals using fuzzy bernstein polynomials

Author

Listed:
  • Reza Ezzati

    (Islamic Azad University)

  • Shokrollah Ziari

    (Islamic Azad University)

Abstract

In this paper, we approximate the integration of continuous fuzzy real number valued function of one and two variables. To do this, we use Bernstein-type fuzzy polynomials. Moreover, we obtain the error estimates for these approximations in terms of the modulus of continuity.

Suggested Citation

  • Reza Ezzati & Shokrollah Ziari, 2012. "Approximation of fuzzy integrals using fuzzy bernstein polynomials," Fuzzy Information and Engineering, Springer, vol. 4(4), pages 415-423, December.
  • Handle: RePEc:spr:fuzinf:v:4:y:2012:i:4:d:10.1007_s12543-012-0124-y
    DOI: 10.1007/s12543-012-0124-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12543-012-0124-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s12543-012-0124-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tuan Nguyen Dinh, 2023. "Regularity of Multipliers for Multiobjective Optimal Control Problems Governed by Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 762-796, February.
    2. Guillermo Ayala & María Concepción López-Díaz & Miguel López-Díaz & Lucía Martínez-Costa, 2015. "Methods and Algorithms to Test the Hausdorff and Simplex Dispersion Orders with an R Package," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 661-675, September.
    3. Emmanuel Lepinette, 2020. "Random optimization on random sets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 159-173, February.
    4. Jinping Zhang & Keming Zhang, 2022. "Portfolio selection models based on interval-valued conditional value at risk (ICVaR) and empirical analysis," Papers 2201.02987, arXiv.org, revised Jul 2022.
    5. Lopez-Diaz, Miguel & Rodriguez-Muniz, Luis J., 2007. "Influence diagrams with super value nodes involving imprecise information," European Journal of Operational Research, Elsevier, vol. 179(1), pages 203-219, May.
    6. Ilya Molchanov & Anja Muhlemann, 2019. "Nonlinear expectations of random sets," Papers 1903.04901, arXiv.org.
    7. Ayala, Guillermo & López-Díaz, Miguel, 2009. "The simplex dispersion ordering and its application to the evaluation of human corneal endothelia," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1447-1464, August.
    8. Pascal Bianchi & Walid Hachem, 2016. "Dynamical Behavior of a Stochastic Forward–Backward Algorithm Using Random Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 90-120, October.
    9. Rodríguez-Muñiz, Luis J. & López-Díaz, Miguel, 2007. "On the exchange of iterated expectations of random upper semicontinuous functions," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1628-1635, October.
    10. Jérôme Couvreux & Christian Hess, 1999. "A Lévy Type Martingale Convergence Theorem for Random Sets with Unbounded Values," Journal of Theoretical Probability, Springer, vol. 12(4), pages 933-969, October.
    11. Yan Sun & Guanghua Lian & Zudi Lu & Jennifer Loveland & Isaac Blackhurst, 2020. "Modeling the Variance of Return Intervals Toward Volatility Prediction," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 492-519, July.
    12. M. Guo & X. Xue & R. Li, 2004. "Controllability of Impulsive Evolution Inclusions with Nonlocal Conditions," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 355-374, February.
    13. Wang, Rongming & Wang, Zhenpeng, 1997. "Set-Valued Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 180-198, October.
    14. Castaing, Charles & Quang, Nguyen Van & Thuan, Nguyen Tran, 2012. "A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 84-95.
    15. Ezzaki, Fatima & Tahri, Khalid, 2019. "Representation theorem of set valued regular martingale: Application to the convergence of set valued martingale," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    16. Tito Homem-de-Mello, 2001. "Estimation of Derivatives of Nonsmooth Performance Measures in Regenerative Systems," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 741-768, November.
    17. Tourky, Rabee & Yannelis, Nicholas C., 2001. "Markets with Many More Agents than Commodities: Aumann's "Hidden" Assumption," Journal of Economic Theory, Elsevier, vol. 101(1), pages 189-221, November.
    18. Emmanuel Lepinette & Ilya Molchanov, 2017. "Conditional cores and conditional convex hulls of random sets," Papers 1711.10303, arXiv.org.
    19. Li Guan & Juan Wei & Hui Min & Junfei Zhang, 2021. "The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space," Mathematics, MDPI, vol. 9(11), pages 1-12, May.
    20. López-Díaz, Miguel, 2006. "An indexed multivariate dispersion ordering based on the Hausdorff distance," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1623-1637, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:fuzinf:v:4:y:2012:i:4:d:10.1007_s12543-012-0124-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.