International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

An Application of Tripolar \((m,n)\)-Fuzzy Soft Sets in Ordered Semigroups

  • Maliwan Phattarachaleekul
  • Somsak Lekkoksung*

    * Corresponding author

    Abstract

    In this paper, we introduce the concept of tripolar \((m,n)\)-fuzzy soft sets over ordered semigroups. First, we define several core structures, including tripolar \((m, n)\)-fuzzy soft subsemigroups, tripolar \((m, n)\)-fuzzy soft left and right ideals, tripolar \((m, n)\)-fuzzy soft quasi-ideals, and tripolar \((m, n)\)-fuzzy soft bi-ideals, and we also provide concrete examples to clearly explain these new concepts. Second, we present our main results concerning regular ordered semigroups, where we prove that the concepts of a tripolar \((m,n)\)-fuzzy soft quasi-ideal and a tripolar \((m,n)\)-fuzzy soft bi-ideal are identical (they coincide) under regularity. Finally, we characterize tripolar \((m,n)\)-fuzzy soft quasi-ideals by proving that a tripolar \((m,n)\)-fuzzy soft set is a quasi-ideal if and only if it is the intersection of a tripolar \((m,n)\)-fuzzy soft left ideal and a tripolar \((m,n)\)-fuzzy soft right ideal.

    How to Cite

    M. Phattarachaleekul, S. Lekkoksung, An Application of Tripolar \((m,n)\)-Fuzzy Soft Sets in Ordered Semigroups, Int. J. Anal. Appl. 24 (2026), 304. https://doi.org/10.28924/2291-8639-24-2026-304

    BibTeX
    @article{Phattarachaleekul2026,
  author  = {Phattarachaleekul, Maliwan and Lekkoksung, Somsak},
  title   = {An Application of Tripolar \((m,n)\)-Fuzzy Soft Sets in Ordered Semigroups},
  journal = {Int. J. Anal. Appl.},
  volume  = {24},
  year    = {2026},
  pages   = {304},
  doi     = {10.28924/2291-8639-24-2026-304}
}

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