A New Approach to Fuzzy a-Ideals of BCI-Algebras

Ahsan Mahboob and G. Muhiuddin
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Ahsan Mahboob: Department of Mathematics and Statistics, School of Applied Science and Humanities, Vignan’s Foundation for Science, Technology and Research, Vadlamudi, Guntur-522213, India2Department of Mathematics, University of Tabuk, P. O. Box 741, Tabuk 71491, Saudi Arabia
G. Muhiuddin: Department of Mathematics and Statistics, School of Applied Science and Humanities, Vignan’s Foundation for Science, Technology and Research, Vadlamudi, Guntur-522213, India2Department of Mathematics, University of Tabuk, P. O. Box 741, Tabuk 71491, Saudi Arabia

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 02, 677-690

Abstract: To strengthen the ideal theory in BCI-algebras, the more general concept (∈,∈∨(κ∗,q κ))-fuzzy a-ideals in BCI-algebras is proposed. It is shown that (∈,∈∨q)-fuzzy a-ideals are (∈,∈∨(κ∗,q κ))-fuzzy a-ideals; however, the converse is not valid. Following that, the concept of (∈∨(κ∗,q κ),∈∨(κ∗,q κ))-fuzzy a-ideals is introduced. We demonstrate that (∈∨(κ∗,q κ),∈∨(κ∗,q κ))-fuzzy a-ideals are (∈,∈∨(κ∗,q κ))-fuzzy a-ideals. The converse is not true, and an example is given to support it. An equivalent condition for (∈,∈∨(κ∗,q κ))-fuzzy a-ideals is provided. We prove that the (∈,∈∨(κ∗,q κ))-fuzzy a-ideals are (∈,∈∨(κ∗,q κ))-fuzzy p-ideals and (∈,∈∨(κ∗,q κ))-fuzzy q-ideals. Furthermore, (∈,∈∨(κ∗,q κ))-fuzzy a-ideals are characterized in terms a-ideals.

Keywords: BCI-algebras; fuzzy sets; (∈; ∈∨(κ∗; qκ))-fuzzy a-ideals (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500310

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