Neutrosophic UP (BCC)-Subalgebras of Several Types: A  Threshold-Based Analysis in UP (BCC)-Algebras

Aiyared Iampan; Neelamegarajan Rajesh

Authors

Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand;
Neelamegarajan Rajesh Department of Mathematics, Rajah Serfoji Government College, Thanjavur-613005, Tamil Nadu, India;

Keywords:

BCC-algebra; (∈,∈)-neutrosophic BCC-subalgebra; (∈,q)-neutrosophic BCC-subalgebra; (q,∈) neutrosophic BCC-subalgebra; (q,∈)-neutrosophic BCC-subalgebra; (q,∈ ∨q)-neutrosophic BCC-subalgebra

Abstract

This paper presents a comprehensive exploration of neutrosophic UP-subalgebras within the frame
work of BCC-algebras, introducing a novel framework for their classification and characterization. By in
tegrating neutrosophic set theory—which generalizes fuzzy and intuitionistic fuzzy sets—we systematically
investigate three types of neutrosophic subalgebras: (∈,∈)-neutrosophic, (q,∈ ∨q)-neutrosophic, and their hy
brid variants. A key contribution lies in establishing rigorous conditions under which neutrosophic ∈-subsets,
q-subsets, and ∈ ∨q-subsets qualify as BCC-subalgebras, leveraging threshold-based analysis (e.g., λ, µ, ν
parameters) to delineate membership and non-membership criteria. We further derive algebraic characteriza
tions for (Φ,Ψ)-neutrosophic BCC-subalgebras, where Φ,Ψ ∈ {∈,q,∈ ∨q}, and demonstrate their theoretical
consistency through illustrative examples and counterexamples. Notably, the study reveals that neutrosophic
q-subsets and ∈ ∨q-subsets exhibit subalgebraic properties under specific threshold constraints (λ,µ > 0.5;
ν < 0.5), extending classical results in fuzzy algebraic structures. Our findings contribute to the theoretical
foundations of neutrosophic algebraic systems while offering a versatile tool for modeling uncertainty in logical
algebras, decision-making, and beyond.

DOI 10.5281/zenodo.17216439.