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Generalizations of Fuzzy q‐Ideals of BCI‐Algebras

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  • G. Muhiuddin
  • D. Al-Kadi
  • A. Mahboob
  • A. Assiry
  • Abdullah Alsubhi

Abstract

In this paper, we introduce the notion of (∈, ∈∨(κ∗, qκ))‐fuzzy q‐ideals of BCI‐algebras to propose a more general form of fuzzy q‐ideals of BCI‐algebras. We prove that (∈, ∈∨q)‐fuzzy q‐ideals and (∈∨(κ∗, qκ), ∈∨(κ∗, qκ))‐fuzzy q‐ideals are (∈, ∈∨(κ∗, qκ))‐fuzzy q‐ideals, but the converse assertion is not valid and examples are given to support this. It is proved that every (∈, ∈∨(κ∗, qκ))‐fuzzy q‐ideal is an (∈, ∈∨(κ∗, qκ))‐fuzzy ideal, but the converse need not be true in general and an example is provided. In addition, correspondence between (∈, ∈∨(κ∗, qκ))‐fuzzy q‐ideals and q‐ideals of BCI‐algebras is considered.

Suggested Citation

  • G. Muhiuddin & D. Al-Kadi & A. Mahboob & A. Assiry & Abdullah Alsubhi, 2022. "Generalizations of Fuzzy q‐Ideals of BCI‐Algebras," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:2388199
    DOI: 10.1155/2022/2388199
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    References listed on IDEAS

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    1. G. Muhiuddin & D. Al-Kadi & A. Mahboob & Ali Jaballah, 2020. "Hybrid Structures Applied to Ideals in BCI-Algebras," Journal of Mathematics, Hindawi, vol. 2020, pages 1-7, November.
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