IDEAS home Printed from https://ideas.repec.org/p/ems/eureri/30923.html
   My bibliography  Save this paper

Function Approximation Using Probabilistic Fuzzy Systems

Author

Listed:
  • van den Berg, J.H.
  • Kaymak, U.
  • Almeida e Santos Nogueira, R.J.

Abstract

We consider function approximation by fuzzy systems. Fuzzy systems are typically used for approximating deterministic functions, in which the stochastic uncertainty is ignored. We propose probabilistic fuzzy systems in which the probabilistic nature of uncertainty is taken into account. Furthermore, these systems take also fuzzy uncertainty into account by their fuzzy partitioning of input and output spaces. We discuss an additive reasoning scheme for probabilistic fuzzy systems that leads to the estimation of conditional probability densities, and prove how such fuzzy systems compute the expected value of this conditional density function. We show that some of the most commonly used fuzzy systems can compute the same expected output value and we derive how their parameters should be selected in order to achieve this goal.

Suggested Citation

  • van den Berg, J.H. & Kaymak, U. & Almeida e Santos Nogueira, R.J., 2011. "Function Approximation Using Probabilistic Fuzzy Systems," ERIM Report Series Research in Management ERS-2011-026-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:30923
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/30923/ERS-2011-026-LIS.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. van den Berg, J.H. & van den Bergh, W.-M. & Kaymak, U., 2001. "Probabilistic and Statistical Fuzzy Set Foundations of Competitive Exception Learning," ERIM Report Series Research in Management ERS-2001-40-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    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. van den Berg, J.H. & van den Bergh, W.-M. & Kaymak, U., 2003. "Financial Markets Analysis by Probabilistic Fuzzy Modelling," ERIM Report Series Research in Management ERS-2003-036-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Loquin, Kevin & Strauss, Olivier, 2008. "Histogram density estimators based upon a fuzzy partition," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1863-1868, September.

    More about this item

    Keywords

    additive reasoning; function approximation; fuzzy partitioning; fuzzy set; probabilistic fuzzy system;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ems:eureri:30923. 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: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/erimanl.html .

    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.