(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The ordered semigroups are algebraic systems consisting of a non-empty set, an associative binary operation, and a partial order compatible with this binary operation. Grosek and Stako studied almost ideals in semigroups in 1980. In 2019 S. Suebsung et al. studied almost (m; n)-ideals in semigroups. Later, in 2022, S. Suebsung et al. introduced almost ideals in ordered semigroups. This paper aims to de ne almost (m; n)-quasi-ideals and fuzzy almost (m; n)-quasi-ideals in ordered semigroups. We prove the union of almost (m; n)-quasi-ideals, including almost (m; n)-quasi-ideals in ordered semigroups. In class, fuzzications are the same. Finally, we connect relation almost (m; n)-quasi-ideals and fuzzy almost (m; n)-quasi-ideals in ordered semigroups.