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Open Access Research Article

True-False ideals of BCK/BCI-algebras

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pp. 45–62Vol. 27Issue 1January 2024DOI: 10.47974/JDMSC-1544 Crossmark XML
Received:
11 May 2021
Accepted:
20 Oct 2021
Published Online:
24 Jan 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1544
Pages:
45–62

Abstract

The notions of a (limited) T & F-ideal and a T & F--subalgebra are introduced, and various properties are investigated. The relationship between a T & F-subalgebra and a T & F-ideal is established. Conditions for a T & F-structure (resp., T & F-subalgebra) to be a T & F-ideal are discussed. An example is provided to confirm that in a BCI-algebra, a T & F-ideal cannot be a T & F-subalgebra in general, and then conditions for a T & F-ideal to be a T & F-subalgebra in a BCI-algebra are considered. The relationship between a T & F-ideal and a T & F--subalgebra in a BCK-algebra with condition (S) is discussed. Conditions for a T & F-structure over a BCK-algebra with condition (S) to be a T & F-ideal are provided. Using the notion of T & F-level sets, a characterization of a T & F-ideal is established. A novel T & F-ideal is constructed with an existing T & F-ideal using a characterization of a T & F-ideal. 

Keywords

Subject Classifications

(2010) 03G2506F3503E7208A72

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