Study on the lattice order-related properties of a class of vector sets with state attributes. A lattice is a kind of special partially ordered set. The state space of a power system is abstracted as a class of vector sets with state attributes. Furthermore, under a class of partial orders based on positional relations, the lattice-order properties of this class of vector sets with state attributes are proven, including lattice, bounded lattice, complete lattice, and distributive lattice, and some examples are also provided to explain the main results. Research results can provide theoretical and methodological support for the effective partitioning of the state space of large-scale complex power systems, state screening for reliability assessment, and research on efficient algorithms.