IDEAS home Printed from https://ideas.repec.org/a/wsi/nmncxx/v18y2022i03ns1793005722500429.html
   My bibliography  Save this article

On Minimal Fuzzy Realization in Category Theoretic Setting

Author

Listed:
  • Shailendra Singh

    (Department of Mathematics & Computing, Indian Institute of Technology (ISM), Dhanbad 826004, India)

  • Amarjit Kaur Sahni

    (Department of Mathematics, AIAS, Amity University, UP, India)

  • Jayanti Tripathi Pandey

    (Department of Mathematics, AIAS, Amity University, UP, India)

Abstract

This paper aims to study the minimal fuzzy realization for a fuzzy language with membership values in a complete residuated lattice by using category theory. Specifically, we introduce the concept of a category 𠒞𠒯ℛℒ(Σ), whose object-class is complete transition residuated lattices corresponding to deterministic Σ-semiautomata. We give the categorical characterization of reachability and observability maps for a given deterministic fuzzy automaton. In another direction, we demonstrate that the category 𠒟𠒮𠒜(Σ) is a subcategory of the categories ℱ𠒞𠒜(Σ) of F1-coalgebras and ℱ𠒟𠒜(Σ) of (F2,F3)-dialgebras. Also, we discuss the concept of bisimulation between F1-coalgebras. Next, we introduce a general theory of minimal fuzzy realization for a given fuzzy language in a category theory setting. Strikingly, we demonstrate that all minimal fuzzy realization for a given fuzzy language is one of a kind up to isomorphism.

Suggested Citation

  • Shailendra Singh & Amarjit Kaur Sahni & Jayanti Tripathi Pandey, 2022. "On Minimal Fuzzy Realization in Category Theoretic Setting," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 889-917, November.
    • Handle: RePEc:wsi:nmncxx:v:18:y:2022:i:03:n:s1793005722500429
    DOI: 10.1142/S1793005722500429
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S1793005722500429
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S1793005722500429?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.

    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:wsi:nmncxx:v:18:y:2022:i:03:n:s1793005722500429. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/nmnc/nmnc.shtml .

    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.