1MathematicsDepartment, Acharya Nagarjuna University, Nagarjuna Nagar, India
2BS & H Department, SR Gudlavalleru Engineering College, Gudlavalleru, India
3Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaih Educational
Foundation, Vaddeswaram-522302, Guntur(DT), Andhra Pradesh, India
4Faculty of Information Systems and Computer Science, October 6th University, Giza, 12585, Egypt
5Faculty of Informatics, Midocean University by Everyone's Smart University, 3999, Fujairah, United Arab Emirates
6Faculty of Information Systems and Computer Science, October 6th University, Giza, 12585, Egypt;
7Faculty of Informatics, Midocean University by Everyone's Smart University, 3999, Fujairah, United Arab Emirates
Emails: drbsn63@yahoo.co.in; rajanipapers@gmail.com; ram.fuzzy@gmail.com; aahafeez.scis@o6u.edu.eg; abdelrhman.refaat@midocean.ae; Kmensh.csis@o6u.edu.eg; Khaled@midocean.ae
*Corresponding author: rajanipapers@gmail.com
Abstract
The foundational concepts of subalgebra, ideal, and homomorphism within the domain of BF-algebra were originally introduced by Andrzej Walendziak [A. Walendziak, On BF-Algebras, Math. Slovaca, 57(2) (2007), 119-128]. In this paper, we introduce innovative concepts related to Neutrosophic BF-Subalgebras and Neutrosophic BF-Ideals derived from the application of Subalgebra, Ideal, and Homomorphism principles to Neutrosophic sets. We explore the outcomes concerning a Neutrosophic BF-Ideal with respect to principle of homomorphism, homomorphic image of a Neutrosophic BF-Ideal satisfying the sup-inf property, and homomorphic pre-images within the context of a Neutrosophic set embedded in BF-algebra. The outcomes of the above study are equally applicable to Neutrosophic BF-Subalgebra Lastly, we delve into the conceptual understanding of a level set of a Neutrosophic BF-Ideal within a BF-algebra. In the future, the above study can be extended to address various types of implicative ideals and filters within BF-algebra. Moreover, these Neutrosophic BF-Subalgebras and Neutrosophic BF-Ideals can be applied to neutrosophic soft sets within the context of BF-algebra, which are used for various decision making techniques.
Keywords: BF-algebra; Ideals; Subalgebras; Homomorphism; Neutrosophic BF-Subalgebra; Neutrosophic BF-Ideal.