Abstract
The notions of interior BCK/BCI-algebras, positive implicative interior BCK-algebras, (weak) interior ideals, positive implicative interior ideals, a positive implicative weak interior ideal of type 1, type 2, and type 3 are introduced, and related properties are investigated. A mapping is provided to the set of all involutions of a bounded BCK-algebra in relation to any interior BCK-algebra so that the set of all involutions of a bounded BCK-algebra can be an interior BCK-algebra. The relationship between interior ideals, weak interior ideals, and positive implicative interior ideals is established. The conditions under which a weak interior ideal can change to an interior ideal are founded. The conditions for an interior ideal to be a positive implicative interior ideal are provided. The scalability for a positive implicative interior ideal is discussed. The relationship between type 1, type 2, and type 3 on positive implicative weak interior ideals are investigated. The relationship between weak interior ideal and positive implicative weak interior ideal of type 1, type 2, and type 3 are established.
Original language | English |
---|---|
Pages (from-to) | 1923-1933 |
Number of pages | 11 |
Journal | International Journal of Computational Intelligence Systems |
Volume | 14 |
Issue number | 1 |
DOIs | |
State | Published - 2021 |
Keywords
- (weak) interior ideals Positive implicative interior ideals
- Interior BCK/BCI-algebras
- Positive implicative interior BCK-algebras
- Positive implicative weak interior ideal of type 1 Type 2 And type 3