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

Author

Listed:
  • Ahsan Mahboob

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
    All authors contributed equally to this work.)

  • Abdus Salam

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
    All authors contributed equally to this work.)

  • Md. Firoj Ali

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
    All authors contributed equally to this work.)

  • Noor Mohammad Khan

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
    All authors contributed equally to this work.)

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.

Suggested Citation

  • Ahsan Mahboob & Abdus Salam & Md. Firoj Ali & Noor Mohammad Khan, 2019. "Characterizations of Regular Ordered Semigroups by (∈,∈∨( k ∗ , q k ))-Fuzzy Quasi-Ideals," Mathematics, MDPI, vol. 7(5), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:401-:d:228378
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    References listed on IDEAS

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    1. M. Shabir & A. Khan, 2008. "Characterizations Of Ordered Semigroups By The Properties Of Their Fuzzy Generalized Bi-Ideals," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 237-250.
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