Characterizations of Regular Ordered Semigroups by (∈,∈∨(k∗,qk))-Fuzzy Quasi-Ideals

Abstract

In this paper, some properties of the ( k ∗ , k ) -lower part of ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideals are obtained. Then, we characterize regular ordered semigroups in terms of its ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideals, ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy generalized bi-ideals, ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy left ideals and ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy right ideals, and an equivalent condition for ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy left (resp. right) ideals is obtained. Finally, the existence theorems for an ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideal as well as for the minimality of an ( ∈ , ∈ ∨ ( k ∗ , q k ) ) -fuzzy quasi-ideal of an ordered semigroup are provided.

On Interval Valued Fuzzy Bi-interior Ideals in Semigroups

“…Rao [5] introduced and studied the definition and properties of the bi-interior ideal in the semigroup. In 2019, A. Mahboob et al [8] characterizations of regular ordered semigroups by (ε, ε (k,qk) )-fuzzy quasi ideals. G Muhiuddin et al discussed a new type of fuzzy semiprime subsets in ordered semigroups.…”

Characterizations of Ordered Semigroups in Terms of Anti-fuzzy Ideals

“…Recent developments in fuzzy ideals related to semigroups and hemirings have prompted the formulation of a precise description of numerous classes of semigroups and hemirings and their characterizations (see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]). Moreover, new classifications of ordered semigroups have been investigated by introducing the concept of ( ∈ , ∈ ∨(k * , q k ))-fuzzy subsystems and ( ∈ , ∈ ∨(k * , q k ))-fuzzy quasi-ideals by Khan et al [27] and Mahboob et al [28], respectively.…”