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Soft Ideals And Generalized Fuzzy Ideals In Semigroups

Author

Listed:
  • MUHAMMAD SHABIR

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

  • MUHAMMAD IRFAN ALI

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

Abstract

A soft semigroup over a semigroup is a collection of subsemigroups. Similarly, a soft ideal over a semigroup is a collection of ideals of the semigroup. As a natural consequence, the idea of soft ideals of a soft semigroup originates. Soft ideals over a semigroup with a fixed set of parameters form a distributive lattice. Soft sets are a very handy tool. Soft ideals over a semigroup characterize generalized fuzzy ideals and fuzzy ideals with thresholds ofS.

Suggested Citation

  • Muhammad Shabir & Muhammad Irfan Ali, 2009. "Soft Ideals And Generalized Fuzzy Ideals In Semigroups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 599-615.
    • Handle: RePEc:wsi:nmncxx:v:05:y:2009:i:03:n:s1793005709001544
    DOI: 10.1142/S1793005709001544
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    Citations

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    Cited by:

    1. Samaher Adnan Abdul-Ghani & Shuker Mahmood Khalil & Mayadah Abd Ulrazaq & Abu Firas Muhammad Jawad Al-Musawi, 2018. "New Branch of Intuitionistic Fuzzification in Algebras with Their Applications," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2018, pages 1-6, July.
    2. Muhammad Shabir & Rimsha Mushtaq & Muhammad Jawad & Munazza Naz & Fahd Jarad & Thabet Abdeljawad, 2023. "Int N-Soft Substructures of Semigroups," Mathematics, MDPI, vol. 11(2), pages 1-23, January.
    3. Arif Mehmood Khattak & Gulzar Ali Khan & Mujeeb Ur Rehman & Sameena Nadeem & Muhammad Safeer, 2018. "P-Separation Axioms In Supra Soft Topological Space," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(2), pages 7-10, January.
    4. Wei Yang, 2013. "New similarity measures for soft sets and their application," Fuzzy Information and Engineering, Springer, vol. 5(1), pages 19-25, March.
    5. H. Hazra & P. Majumdar & S. K. Samanta, 2012. "Soft topology," Fuzzy Information and Engineering, Springer, vol. 4(1), pages 105-115, March.

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