Open AccessArticle

Generalizations of implication-based fuzzy subalgebras in BCK/BCI-algebras

and

Young Bae Jun¹

1Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia.

* Corresponding Author: G. Muhiuddin. Email: chishtygm@gmail.com

Annals of Communications in Mathematics 2021, 4 (2), 180-189. https://doi.org/10.62072/acm.2021.040211

Received: 15 May 2021 |

Accepted: 2 August 2021 |

Published: 30 September 2021

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Abstract

In [2], Jun discussed implication-based subalgebras in BCK/BCI-algebras. In this article, more general forms than Jun’s results are discussed. We provide an example to show that a fuzzy subalgebra with thresholds 0 and 0.5 is not an implication-based subalgebra under the Łuckasiewicz implication operator, and then conditions for a fuzzy subalgebra with thresholds 0 and 0.5 to be an implication-based subalgebra under the Łuckasiewicz implication operator are provided.

Keywords

Fuzzifying subalgebra; Fuzzy subalgebra with thresholds ε and δ; t-implicationbased subalgebra

Cite This Article

G. Muhiuddin, Young Bae Jun.

Generalizations of implication-based fuzzy subalgebras in BCK/BCI-algebras.

Annals of Communications in Mathematics

2021,

4 (2):

180-189.

https://doi.org/10.62072/acm.2021.040211

Copyright © 2021 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).