Algebraic Aspects of Crossing Cubic BE-Algebras

• Published in: Fuzzy information and engineering Vol. 17; no. 1; pp. 20 - 38
• Main Authors: Al-Rahman, Noor Bani Abd, Al-Masarwah, Anas, Alkouri, Abd Ulazeez
• Format: Journal Article
• Language: English
• Published: Tsinghua University Press 01.03.2025
• Subjects: be-algebras; crossing cubic filters; crossing cubic structures; crossing cubic subalgebras; weak crossing cubic subalgebras
• ISSN: 1616-8658; 1616-8666
• DOI: 10.26599/FIE.2025.9270051

Recently, interval-valued fuzziness and negative structures have gained popularity among researchers and have been widely used in algebraic structures such as semigroups, rings, and lattices. The crossing cubic structure (CC) is an expansion of a bipolar fuzziness structure and a parallel circuit between interval-valued fuzziness and negative structures. The main objective of this study is to apply the idea of CCs to BE-algebras. In the present research, we modify and extend the notions of fuzziness algebraic substructures, namely subalgebras, weak subalgebras and filters of BE-algebras to introduce the notions of crossing cubic subalgebras (CCSs), weak crossing cubic subalgebras (WCCSs), and crossing cubic filters (CCFs) in BE-algebras, and we probe several characteristics of these notions. Furthermore, the relationship between CCSs, WCCSs, and CCFs in BE-algebras is established. After that, the conditions under which CCs can be CCS and CCF, and the condition under which WCCS can be CCS are discovered. At last, some characterizations of CCF in BE-algebras are presented.