Advanced Partitioned Neutrosophic Sets: Formalization of Hexa-, Hepta-, Octa-, Nona-, and Deca-Partitioned Structures

Abstract

Uncertainty‐modeling frameworks such as fuzzy sets, intuitionistic fuzzy sets, hyperfuzzy sets, neutrosophic sets, and plithogenic sets have been widely adopted for representing and reasoning under vagueness and imprecision. Neutrosophic sets assign each element three independent membership values—truth, indeterminacy, and falsity—and their partitioned extensions introduce additional components, subject to sum‐boundedconstraints. Notable examples include quadripartitioned, pentapartitioned, and heptapartitioned neutrosophic sets. In this work, we formally define the hexa‐, octa‐,
nona‐, and decapartitioned neutrosophic sets and prove that each can be naturally embedded within the plithogenic set framework. This unifying representation facilitates a comprehensive approach to neutrosophic set theory and broadens its potential applications.