Malaysian Journal of Mathematical Sciences, December 2023, Vol. 17, No. 4
$n$-polar $Z$-hesitant Complementary Fuzzy Soft Set in BCK/BCI-Algebras
Alsager, K. M.
Corresponding Email: ksakr@qu.edu.sa
Received date: 15 October 2023
Accepted date: 14 November 2023
Abstract:
This paper introduces an innovative concept known as $n$-polar $Z$-hesitant Anti-Fuzzy Soft Sets (MZHAFSs) within the framework of BCK/BCI-algebras. Soft set theory originates in the captivating field of fuzzy set theory. Our approach is a harmonious synthesis of $n$-polar anti-fuzzy set theory, soft set models, and $Z$-hesitant anti-fuzzy sets, skillfully applied within the framework of BCK/BCI-algebras. This effort leads to the introduction of a new variant of fuzzy sets termed MZHAFSs ($n$-polar $Z$-hesitant anti-fuzzy soft sets) in the context of BCK/BCI-algebras. Additionally, we elucidate the concept of $n$-polar $Z$-hesitant anti-fuzzy soft sets to provide a comprehensive understanding. Furthermore, we introduce and define various related concepts, including $n$-polar $Z$-hesitant anti-fuzzy soft subalgebras, $n$-polar $Z$-hesitant anti-fuzzy soft ideals, $n$-polar $Z$-hesitant anti-fuzzy soft closed ideals, and $n$-polar $Z$-hesitant anti-fuzzy soft commutative ideals, and establish meaningful connections between them. We also present and rigorously prove several theorems that are pertinent to these newly introduced notions.
Keywords: $n$-polar $Z$-hesitant anti-fuzzy sets; fuzzy logic; fuzzy control
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