Note for Quadripartitioned Neutrosophic Offset, Pentapartitioned Neutrosophic Offset, and Heptapartitioned Neutrosophic Offset

Neutrosophic sets assign each element three independent membership values—truth, indeterminacy, and falsity—and their partitioned extensions introduce additional components subject to sum-bounded constraints. Notable examples include quadripartitioned, pentapartitioned, and heptapartitioned neutrosophic sets. The O set concept further extends this framework by allowing membership values outside the standard [0, 1] interval, including negative values and values exceeding one. In this paper, we introduce and analyze the Quadripartitioned Neutrosophic O set, Pentapartitioned Neutrosophic O set, and Heptapartitioned Neutrosophic O set. These extensions are intended to enhance the expressiveness of neutrosophic theory and to stimulate further research in neutrosophic and fuzzy uncertainty.