Quantcast

Mathematics, Vol. 7, Pages 401: Characterizations of Regular Ordered Semigroups by (∈,∈∨(k*,qk))-Fuzzy Quasi-Ideals

Research paper by Ahsan Mahboob, Abdus Salam, Md. Ali, Noor Khan

Indexed on: 08 May '19Published on: 05 May '19Published in: Mathematics



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.