International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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Volume 26 , Issue 2 , PP: 164-181, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Principal L-fuzzy ideals and filters on a trellis

Sarra Boudaoud 1 , Lemnaouar Zedam 2 , Soheyb Milles 3 *

  • 1 Laboratory of Pure and Applied Mathematics, Faculty of Mathematics and Computer Science, University of M’sila, University Pole, Raod Bordj Bou Arreridj, M’sila 28000, Algeria - (sarra.boudaoud@univ-msila.dz)
  • 2 Laboratory of Pure and Applied Mathematics, Faculty of Mathematics and Computer Science, University of M’sila, University Pole, Raod Bordj Bou Arreridj, M’sila 28000, Algeria - (lemnaouar.zedam@univ-msila.dz)
  • 3 Laboratory of Science for Mathematics, Computer Science and Engineering Applications, Department of Mathematics, University Center of Barika, Amdoukal Road, Barika, 05001, Algeria - (soheyb.milles@cu-barika.dz)
  • Doi: https://doi.org/10.54216/IJNS.260212

    Received: December 14, 2024 Revised: February 14, 2025 Accepted: March 11, 2025
    Abstract

    In this paper, we study the notion of principal (crisp) fuzzy ideals (resp. filters) on the setting of trellises (or weakly associative lattices as called by several authors). More specifically, we introduce the notions of L-fuzzy ideals and L-fuzzy filters on a given trellis and provide basic characterizations of these notions based on their weakly associative meet and join operations. We pay particular attention to the kind of principal L-fuzzy ideals (resp. filters) on a given trellis, which are more complicated in the absence of the (associativity) transitivity property.

    Keywords :

    Trellis , Lattice , Fuzzy set , Principal ideal , Principal filter

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    Cite This Article As :
    Boudaoud, Sarra. , Zedam, Lemnaouar. , Milles, Soheyb. Principal L-fuzzy ideals and filters on a trellis. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 164-181. DOI: https://doi.org/10.54216/IJNS.260212
    Boudaoud, S. Zedam, L. Milles, S. (2025). Principal L-fuzzy ideals and filters on a trellis. International Journal of Neutrosophic Science, (), 164-181. DOI: https://doi.org/10.54216/IJNS.260212
    Boudaoud, Sarra. Zedam, Lemnaouar. Milles, Soheyb. Principal L-fuzzy ideals and filters on a trellis. International Journal of Neutrosophic Science , no. (2025): 164-181. DOI: https://doi.org/10.54216/IJNS.260212
    Boudaoud, S. , Zedam, L. , Milles, S. (2025) . Principal L-fuzzy ideals and filters on a trellis. International Journal of Neutrosophic Science , () , 164-181 . DOI: https://doi.org/10.54216/IJNS.260212
    Boudaoud S. , Zedam L. , Milles S. [2025]. Principal L-fuzzy ideals and filters on a trellis. International Journal of Neutrosophic Science. (): 164-181. DOI: https://doi.org/10.54216/IJNS.260212
    Boudaoud, S. Zedam, L. Milles, S. "Principal L-fuzzy ideals and filters on a trellis," International Journal of Neutrosophic Science, vol. , no. , pp. 164-181, 2025. DOI: https://doi.org/10.54216/IJNS.260212