A Comparative Study of Neutrosophic Subalgebras in
Sheffer Stroke UP-algebras
Aiyared Iampan1,∗, Vennila Ramasamy2, V. Vijaya Bharathi3, K. Geetha4, Neelamegarajan Rajesh4
1Department of Mathematics, School of Science, University of Phayao, 19 Moo 2, Mae Ka, Mueang, Phayao
56000, Thailand
2Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore-641202, Tamil Nadu, India
3Department of Mathematics, Sri Sarada College for Women (Autonomous), Salem-636016, Tamil Nadu,
India
4Department of Mathematics, Rajah Serfoji Government College (affiliated to Bharathidasan University),
Thanjavur-613005, Tamil Nadu, India
Emails: aiyared.ia@up.ac.th; vennilamaths@gmail.com; vijayabharathi v@yahoo.com;
geeethaak@gmail.com; nrajesh topology@yahoo.co.in
Abstract
In this paper, we conduct a comprehensive study of neutrosophic subalgebras of various types within the
framework of Sheffer stroke UP-algebras (SUP-algebras). Specifically, we introduce and characterize (∈, ∈),
(∈, ∈ ∨q), and (q, ∈ ∨q)-neutrosophic subalgebras based on neutrosophic ∈-subsets, q-subsets, and (∈ ∨q)-
subsets. Necessary and sufficient conditions are established for these subsets to form subalgebras under the
Sheffer stroke operation. Several theorems demonstrate how these types interrelate and differ in their structural
properties, with illustrative examples provided. Furthermore, we identify the conditions under which certain
canonical subsets, such as X1
0 = {x ∈ X | T (x) > 0, I(x) > 0, F (x) < 1}, form subalgebras across differ-
ent neutrosophic configurations. These results offer a unified perspective and deeper insight into the algebraic
behavior of neutrosophic systems in the context of SUP-algebras.
Keywords: Neutrosophic set; Neutrosophic ∈-subset; Neutrosophic q-subset; Neutrosophic ∈ ∨q-subset;
(∈, ∈)-neutrosophic subalgebra; (∈, q)-neutrosophic subalgebra; (q, ∈)-neutrosophic subalgebra; (q, ∈ ∨q)-
neutrosophic subalgebra