IDEAS home Printed from https://ideas.repec.org/a/taf/tsysxx/v56y2025i16p4157-4169.html
   My bibliography  Save this article

Nonuniqueness of mathematical models of the simplest three-input Mamdani fuzzy proportional-integral-derivative controllers

Author

Listed:
  • Sadhna Malik
  • B. M. Mohan

Abstract

Mathematical modelling of various fuzzy controllers has been extensively researched and well-documented. As a result, it is well-known that the model of a fuzzy controller depends on several factors, including AND operator, OR operator, inference method, aggregation operator, and defuzzification method. As it appears from the literature, Maximum (Max) aggregation operator has been often used in the modelling of fuzzy controllers. However, utilisation of Bounded Sum (BS) aggregation operator has been rarely seen. This paper aims to address three important issues: (i) studying the characteristics of three-input fuzzy Proportional-Integral-Derivative (PID) controllers developed via BS aggregation operator, (ii) studying the uniqueness of all 14 possible three-input fuzzy PID controllers, and (iii) studying the computational aspects of unique controllers. Surprisingly, it has been observed that the controllers developed using the BS aggregation operator are not unique. Moreover, out of 14 controllers, only nine have been identified as distinct and appropriate for control purposes, while one controller has been deemed unsuitable for control.

Suggested Citation

  • Sadhna Malik & B. M. Mohan, 2025. "Nonuniqueness of mathematical models of the simplest three-input Mamdani fuzzy proportional-integral-derivative controllers," International Journal of Systems Science, Taylor & Francis Journals, vol. 56(16), pages 4157-4169, December.
    • Handle: RePEc:taf:tsysxx:v:56:y:2025:i:16:p:4157-4169
    DOI: 10.1080/00207721.2025.2486158
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00207721.2025.2486158
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00207721.2025.2486158?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

    for a different version of it.

    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:taf:tsysxx:v:56:y:2025:i:16:p:4157-4169. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/TSYS20 .

    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.