α-fuzzy ideals of C-algebra

ABSTRACT

In this paper, we study α-fuzzy ideals in C-algebras whose truth degrees are in a complete Heyting algebra. We provide several characterizations for fuzzy ideals to be an α-fuzzy ideal. One of the key contributions of this manuscript is the investigation of the smallest α-fuzzy ideal containing a given fuzzy ideal. By establishing the existence and properties of this smallest α-fuzzy ideal, we shed light on the structure and behavior of α-fuzzy ideals in C-algebras. Furthermore, we prove that the class of α-fuzzy ideals forms a complete lattice. We obtain the closure operator on the class of fuzzy ideals FI(A), where the closed elements correspond to the α-fuzzy ideals. We explore the conditions under which every fuzzy ideal in a given C-algebra becomes an α-fuzzy ideal. Finally, we study the space of prime α-fuzzy ideals in C-algebras and we derive a necessary and sufficient condition for this space to be a T₁ space.

KEYWORDS:

• C-algebra
• fuzzy ideal
• α-fuzzy ideal
• prime α-fuzzy ideal

MATHEMATICS SUBJECT CLASSIFICATION:

• 03G25
• 03G05
• 08A72

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

No data were used to support this study.

Supplementary Material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/27684830.2024.2352918