₷Ꝗ-Neutrosophic Structures in Semigroup Theory

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.