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A Novel Concept of Fuzzy Subsemigroup (Ideal)

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  • Yu-Hong Che
  • Qi Liu

Abstract

This paper focuses on a generalized definition of fuzzy subsemigroup (ideal) on semigroup. Let L be a completely distributive lattice; we introduce the definition of L‐fuzzy ideal and also the novel concept of subsemigroup (ideal) on semigroup. Then, we discuss the necessary and sufficient conditions of L‐fuzzy subsemigroup (ideal) measure using the four level cuts of an L‐fuzzy set. Moreover, we study the properties of L‐fuzzy subsemigroup (ideal) measure. As an application of L‐fuzzy subsemigroup (ideal) measure, we obtain the L‐fuzzy convexities on a semigroup and bijective semigroup homomorphic mapping is an L‐fuzzy isomorphism.

Suggested Citation

  • Yu-Hong Che & Qi Liu, 2022. "A Novel Concept of Fuzzy Subsemigroup (Ideal)," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:5830590
    DOI: 10.1155/2022/5830590
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    References listed on IDEAS

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    1. Faisal Mehmood & Fu-Gui Shi & Khizar Hayat & Xiao-Peng Yang, 2020. "The Homomorphism Theorems of M -Hazy Rings and Their Induced Fuzzifying Convexities," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    2. Asghar Khan & Young Bae Jun & Tahir Mahmood, 2010. "Generalized Fuzzy Interior Ideals in Abel Grassmann's Groupoids," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-14, March.
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