Advanced Partitioned Neutrosophic Offsets, Oversets, and Undersets: A Formalization of Hexa-, Hepta-, Octa-, Nona-, and Deca-Partitioned Structures

Modern uncertainty-modeling frameworks—fuzzy sets, intuitionistic fuzzy sets, hyperfuzzy sets, neutrosophic sets, and plithogenic sets—provide powerful tools for capturing vagueness and imprecision. In particular, neutrosophic sets characterize each element by three independent degrees: truth, indeterminacy, and falsity. Classical neutrosophic sets have been refined by partitioning the membership degrees into additional components. Recently, the Hexapartitioned Neutrosophic Set, Octapartitioned Neutrosophic Set, Nonapartitioned Neutrosophic Set, and Decapartitioned Neutrosophic Set have been defined. In this paper, we introduce four novel partitioned models—hexapartitioned, octapartitioned, nonapartitioned, and decapartitioned neutrosophic offsets/oversets/undersets—and show how each can be seamlessly embedded into the plithogenic-set framework.