Sun Shin Ahn (Author), Hashem Bordbar (Author), Young Bae Jun (Author)

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 BCKalgebra 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.

Keywords

interior BCK/BCI-algebras;positive implicative interior;BCK-algebras;(weak) interior ideals;positive implicative interior ideals;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UNG - University of Nova Gorica
UDC: 51
COBISS: 71032067 Link will open in a new window
ISSN: 1875-6883
Views: 1119
Downloads: 42
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Other data

URN: URN:SI:UNG
Pages: str. 1923-1933
Volume: ǂVol. ǂ14
Issue: ǂno. ǂ1
Chronology: 2021
DOI: 10.2991/ijcis.d.210622.002
ID: 13160414