IDEAS home Printed from https://ideas.repec.org/a/igg/jfsa00/v6y2017i4p1-20.html
   My bibliography  Save this article

A Valid Scheme to Evaluate Fuzzy Definite Integrals by Applying the CADNA Library

Author

Listed:
  • Mohammad Ali Fariborzi Araghi

    (Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran)

  • Samad Noeiaghdam

    (Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran)

Abstract

The aim of this paper is to estimate the value of a fuzzy integral and to find the optimal step size and nodes via the stochastic arithmetic. For this purpose, the fuzzy Romberg integration rule is considered as an integration rule, then the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method is applied which is a method to describe the discrete stochastic arithmetic. Also, in order to implement this method, the CADNA (Control of Accuracy and Debugging for Numerical Applications) is applied which is a library to perform the CESTAC method automatically. A theorem is proved to show the accuracy of the results by means of the concept of common significant digits. Then, an algorithm is given to perform the proposed idea on sample fuzzy integrals by computing the Hausdorff distance between two fuzzy sequential results which is considered to be an informatical zero in the termination criterion. Three sample fuzzy integrals are evaluated based on the proposed algorithm to find the optimal number of points and validate the results.

Suggested Citation

  • Mohammad Ali Fariborzi Araghi & Samad Noeiaghdam, 2017. "A Valid Scheme to Evaluate Fuzzy Definite Integrals by Applying the CADNA Library," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 6(4), pages 1-20, October.
    • Handle: RePEc:igg:jfsa00:v:6:y:2017:i:4:p:1-20
    as

    Download full text from publisher

    File URL: http://services.igi-global.com/resolvedoi/resolve.aspx?doi=10.4018/IJFSA.2017100101
    Download Restriction: no
    ---><---

    More about this item

    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:igg:jfsa00:v:6:y:2017:i:4:p:1-20. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Journal Editor (email available below). General contact details of provider: https://www.igi-global.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.