₷Ꝗ-Neutrosophic Structures in Semigroup Theory

Mala M; Mary Jansirani M

Authors

Mala M Research Scholar; School of Sciences; Division of Mathematics; SRM- Institute of Science and Technology, Tiruchirappalli Campus, SRM Nagar, Trichy – Chennai Highway, Near Samayapuram, Tiruchirappalli – 621105, Tamil Nadu, India;
Mary Jansirani M Associate Professor; School of Sciences; Division of Mathematics; SRM- Institute of Science and Technology, Tiruchirappalli Campus, SRM Nagar, Trichy – Chennai Highway, Near Samayapuram, Tiruchirappalli – 621105, Tamil Nadu, India;

Keywords:

Neutrosophic set; ₷- ᵴemigroups; ₷- ₣uzzy ᵴemigroups; Ꝗ-₣uzzy set; Ꝗ-₣uzzy ᵴemigroups; ₷Ꝗ-₣uzzy ᵴemigroups; ₷Ꝗ- Neutrosophic ₣uzzy ᵴemigroups(₷Ꝗ-NFS)

Abstract

In this paper, we define and study a new fuzzy algebraic structure called ₷Ꝗ-neutrosophic
fuzzy semigroups (₷Ꝗ-NFS) as a generalization of fuzzy algebra in the framework of ₷-semigroups.
We achieve our objective by introducing a notion called Ꝗ -neutrosophic fuzzy subsets which define
the membership, indeterminacy, and non-membership degree along with a restriction map for each.
With this, we show that the classic fuzzy semigroup theory can be extended to take into account
uncertainty, contradiction, and membership in partial truth degrees all at the same time. We provide
formal definitions, symbolic representations, examples and fundamental propositions that outline
the structure for ₷Ꝗ-NFS. We also look at some features of ₷Ꝗ -NFS that include an identity element
and inverses, demonstrating that we have created a new kind of algebraic system that has both
fuzzy and neutrosophic traits.

DOI: 10.5281/zenodo.16734147