International Journal of Computational Intelligence Systems

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Volume 14, Issue 1, 2021, Pages 1923 - 1933

Interior BCK/BCI-Algebras

Authors
Sun Shin Ahn1, ORCID, Hashem Bordbar2, *, ORCID, Young Bae Jun3, ORCID
1Department of Mathematics Education, Dongguk University, Seoul, 04620, Korea
2Center for Information Technologies and Applied Mathematics, University of Nova Gorica, Nova Gorica, 5000, Slovenia
3Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea
*Corresponding author. Email: hashem.bordbar@ung.si
Corresponding Author
Hashem Bordbar
Received 18 December 2020, Accepted 6 June 2021, Available Online 1 July 2021.
DOI
10.2991/ijcis.d.210622.002How to use a DOI?
Keywords
Interior BCK/BCI-algebras; Positive implicative interior BCK-algebras; (weak) interior ideals; Positive implicative interior ideals; Positive implicative weak interior ideal of type 1, type 2, and type 3
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.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
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Journal
International Journal of Computational Intelligence Systems
Volume-Issue
14 - 1
Pages
1923 - 1933
Publication Date
2021/07/01
ISSN (Online)
1875-6883
ISSN (Print)
1875-6891
DOI
10.2991/ijcis.d.210622.002How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Sun Shin Ahn
AU  - Hashem Bordbar
AU  - Young Bae Jun
PY  - 2021
DA  - 2021/07/01
TI  - Interior BCK/BCI-Algebras
JO  - International Journal of Computational Intelligence Systems
SP  - 1923
EP  - 1933
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.210622.002
DO  - 10.2991/ijcis.d.210622.002
ID  - Ahn2021
ER  -