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

Ahsan Mahboob, Abdus Salam, Md. Firoj Ali and Noor Mohammad Khan
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Ahsan Mahboob: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Abdus Salam: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Md. Firoj Ali: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Noor Mohammad Khan: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Mathematics, 2019, vol. 7, issue 5, 1-16

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.

Keywords: ordered semigroups; fuzzy subsets; (∈,∈∨( k* , qk ))-fuzzy quasi-ideals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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