Noorbhasha Rafi

Fuzzy soft tri-ideals over Gamma-semirings
Annals of Communications in Mathematics 2023
, 6 (4)
, 225-237
DOI: https://doi.org/10.62072/acm.2023.060403
AbstractIn this paper, we introduce the notion of a fuzzy soft tri-ideal over Γ−semiring. We characterize the regular Γ−semiring in terms of fuzzy soft tri-ideals, and study some of the properties. M is a regular Γ−semiring, E be a parameters set and A ⊆ E. If (µ, A) is a fuzzy soft left tri-ideal over M, then (µ, A) is a fuzzy soft right ideal over M.

On Interval Valued Fuzzy Prime Ideals of Γ−semirings
Annals of Communications in Mathematics 2024
, 7 (1)
, 10-20
DOI: https://doi.org/10.62072/acm.2024.070102
AbstractIn this paper, we introduce the notion of interval valued fuzzy prime ideals of Γ−semirings.We study, some properties of prime ideals of a Γ−semirng in terms of interval valued fuzzy ideals.

Ideal Generated by a Translational Invariant Fuzzy Subset And an Element of a Γ−semigroup
Annals of Communications in Mathematics 2024
, 7 (3)
, 241-251
DOI: https://doi.org/10.62072/acm.2024.070302
AbstractIn this section, we introduce the notions of a left and a right translational invariant fuzzy subsets of a Γ−semigroup M, as well as the concept of a unit with respect to a fuzzy subset, and study their properties. We also prove that if μ is a translational invariant fuzzy subset of a commutative Γ−semigroup with unity, then the principal ideal generated by an element and μ that contains a unity element is a prime ideal of the Γ−semigroup.

Tri-quasi ideals and Fuzzy Tri-quasi ideals of Semigroups
Annals of Communications in Mathematics 2024
, 7 (3)
, 281-295
DOI: https://doi.org/10.62072/acm.2024.070307
AbstractIn this paper, we introduce the notion of a tri-quasi ideal and a fuzzy tri-quasi ideal as a further generalization of ideals, left ideals, right ideals, bi-ideals, quasi ideals, and interior ideals. We characterize the regular semigroup in terms of tri-quasi ideals, fuzzy tri-quasi ideals and study some of their properties. This generalization enables mathematicians to explore new relationships and enhancing the understanding of these structures. We establish that, a semigroup is a regular semigroup if and only if B ∩ I ∩ L ⊆ BIL, for any tri-quasi ideal B, ideal I and left ideal L of a semigroup, and for a semigroup, if μ is a fuzzy left tri-ideal of a semigroup then μ is a fuzzy tri-quasi ideal.