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Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals

Author

Listed:
  • Shahida Bashir

    (Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan)

  • Medhit Fatima

    (Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan)

  • Muhammad Shabir

    (Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan)

Abstract

Our main objective is to introduce the innovative concept of ( α , β ) -bipolar fuzzy ideals and ( α , β ) -bipolar fuzzy generalized bi-ideals in ordered ternary semigroups by using the idea of belongingness and quasi-coincidence of an ordered bipolar fuzzy point with a bipolar fuzzy set. In this research, we have proved that if a bipolar fuzzy set h = ( S ; h n , h p ) in an ordered ternary semigroup S is the ( ∈ , ∈ ∨ q ) -bipolar fuzzy generalized bi-ideal of S , it satisfies two particular conditions but the reverse does not hold in general. We have studied the regular ordered ternary semigroups by using the ( ∈ , ∈ ∨ q ) -bipolar fuzzy left (resp. right, lateral and two-sided) ideals and the ( ∈ , ∈ ∨ q ) -bipolar fuzzy generalized bi-ideals.

Suggested Citation

  • Shahida Bashir & Medhit Fatima & Muhammad Shabir, 2019. "Regular Ordered Ternary Semigroups in Terms of Bipolar Fuzzy Ideals," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:233-:d:210841
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    References listed on IDEAS

    as
    1. Kehayopulu, N., 1993. "On regular, intra-regular ordered semigroups," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 4(4), pages 447-461.
    2. 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.
    3. Kehayopulu, N., Lajos, S. & Tsingelis, M., 1993. "On intra-regular ordered semigroups," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 4(3), pages 317-327.
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    Cited by:

    1. Muhammad Shabir & Ahmad N. Al-Kenani & Fawad Javed & Shahida Bashir, 2022. "An Efficient Approach to Approximate Fuzzy Ideals of Semirings Using Bipolar Techniques," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    2. Shahida Bashir & Sundas Shahzadi & Ahmad N. Al-Kenani & Muhammad Shabir, 2021. "Regular and Intra-Regular Semigroups in Terms of m -Polar Fuzzy Environment," Mathematics, MDPI, vol. 9(17), pages 1-18, August.

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