Interior bck/bci-algebras

Sun Shin Ahn, Hashem Bordbar, Young Bae Jun

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1923-1933
Number of pages11
JournalInternational Journal of Computational Intelligence Systems
Volume14
Issue number1
DOIs
StatePublished - 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

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